Luke has taught high school algebra and geometry, college calculus, and has a master's degree in education. In case you were wondering, the vertical line symbo… These unique features make Virtual Nerd a viable alternative to private tutoring. Again, precision of language is key. Please be sure to answer the question.Provide details and share your research! We are already somewhat familiar with set notation: we can pick a solution set from a replacement set. We can also use inequalities, or other statements that might define sets of values or data, to describe the behavior of the variable in set-builder notation.For example, [latex]\left\{x|10\le x<30\right\}[/latex] describes the behavior of [latex]x[/latex] in set-builder notation. Square rooting gives two solutions: `x` must be greater than 2; or `x` must be less than -2: `{x: x > 2 or x < -2}`. Example 1: Compare interval notation with set-builder notation. Another commonly used, and arguably the most concise, method for describing inequalities and solutions to inequalities is called interval notation. There are times when a system of inequalities will not have a solution. Not sure what college you want to attend yet? Download free on the. We are already somewhat familiar with set notation: we can pick a solution set from a replacement set. Test you knowledge afterward with a short quiz. Solving Inequalities Read: { x “such that” x is greater than or equal to negative 7 } Identify the variable used -7 set-builder notation 58. In this non-linear system, users are free to take whatever path through the material best serves their needs. The opening bracket, [, indicates that 80 is included in the solution and is equivalent to saying greater than or equal to. In case you were wondering, the vertical line symbol, |, is translated as the phrase 'such that.' 2 > t 2 > 1 . There are two mathematical notations commonly used to describe the solution sets of compound inequalities: set notation and interval notation. | 11 Share an example of a set described using both systems. This method is widely used and will be present in other math courses you may take.The main concept to remember is that parentheses represent solutions greater or less tha… How to solve basic compound inequalities. The solution set of an inequality can also be described by using set-builder notation . You never know when set notation is going to pop up. Variable: x| 3. Asking for help, clarification, or responding to other answers. The second set describes integers from -3 to 8 (9 is not included). Convert to Interval Notation. We can put an open circle at 80 and draw our arrow to the left showing that all values less than 80 are included. Already registered? What does a compound inequality look like? Moving on, the second notation we can use is called interval notation. Create your account. But avoid …. We want to know if there is a set of solutions for which all three inequalities are true. Get the unbiased info you need to find the right school. Inequalities & Interval Notation. When you represent a set with set notation, you look for a characteristic that identifies the elements of your set. In this non-linear system, users are free to take whatever path through the material best serves their needs. 13 chapters | How this adds anything to the student's understanding, I don't know. Since we want to know where both inequalities are true, we're looking for the area where the shading overlaps, leaving our answer as the purple area in this graph. Write `x^2 - 4 > 0` in its simplest form in set notation. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons These relations are known as strict inequalities, meaning that a is strictly less than or strictly greater than b. Equivalence is excluded. 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Log in here for access. Inequalities & Interval Notation. Support and resources for teaching topics in the new GCSE are available on my website resourceaholic.com. This is in addition to representing solutions on number lines and graphs. Inequalities that include the symbols \(\gt\) or \(\lt\) are called strict inequalities; those that include \(\ge\) or \(\le\) are called nonstrict.. 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The set is the set of all integers exceeding -3 and not greater than 5; this is a finite set; we could write it as a list, The set is even smaller; it contains only five elements: Here are some more examples: The interval can be written as the set looks like this in set notation: or like this Exercise 1. Sciences, Culinary Arts and Personal Inequalities. Interval Notation and Set Builder Notation Calculator: This calculator determines the interval notation and set builder notation for a given numerical statement. Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the set: x: x greater than -8. We've learned that an inequality is just an equation that has a greater than or less than symbol instead of an equals sign, and they help us say things like 'I need at least an 80% to get a B on my history test' or 'the amount of money I spend on video games and plane tickets has to be less than $3,000.' Set notation for inequalities (new GCSE) The new maths GCSE specification states that students will have to represent inequalities using set notation. For example, if you want to describe the set of all number greater than 2 and less than 10, you write {x ∈ R ∣ 2 < x < 10} In either case, a is not equal to b. After you are done with this lesson, you should be able to: To unlock this lesson you must be a Study.com Member. Interval notation Interval notation, on the other hand, describes an interval of values represented by the number line and use parentheses or brackets. Sometimes the set is written with a bar instead of a colon: {`x¦ x > 5`}. You can graph a system of inequalities by working with one inequality at a time. and career path that can help you find the school that's right for you. Question #2 gives the students an opportunity to check their understanding of set builder notation. But we then have to remember that the solution is the space where they are both true. Before we move on, let's talk about two mathematical notations commonly used to describe the solution sets of compound inequalities. Research and discuss the different compound inequalities, particularly unions and intersections. - Definition & Formula, Cost Performance Index vs. Research and discuss the history of infinity. Inequality: x ≤ 5. lessons in math, English, science, history, and more. Compound inequalities involving the word “or” require us to solve each inequality and form the union of each solution set. Strict inequalities without the “or equal to” component are indicated with an open dot on the number line and a parenthesis using interval notation. Next, we graph x < 90 by putting an open circle at 90 and drawing an arrow going to the left to indicate that the answer can be any number smaller than 90. The answer is a finite number of points, written in brackets; for example, {1, 2, 3}.This is the set containing only the elements 1, 2, and 3.But how do we pick a solution set from all the real numbers? 115 lessons But because we are multiplying by a negative number, the inequalities will change direction ... read Solving Inequalities to see why. Compound inequalities that make use of the logical “or” are solved by solutions of either inequality. Convert the inequality to interval notation. Most pre-calculus books and some pre-calculus teachers now require all sets to be written in interval notation. Compare interval notation with set-builder notation. In this non-linear system, users are free to take whatever path through the material best serves their needs. Interval Notation and Set Builder Notation Calculator: This calculator determines the interval notation and set builder notation for a given numerical statement. All rights reserved. Answers are provided. Again, the numbers tell us the bounds, and the brackets and parentheses tell us whether the bound is, or is not, part of the solution. So let's swap them over (and make sure the inequalities still point correctly): 1 < t 2 < 2 Select a subject to preview related courses: The first number is the lower bound, and the second is the upper bound. The solutions to x≥4x≥4 are represented as [4,∞)[4,∞). The first is called set notation. 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There are several different notations used to represent different kinds of inequalities: The notation a < b means that a is less than b. By using this website, you agree to our Cookie Policy. credit by exam that is accepted by over 1,500 colleges and universities. To review, compound inequalities are problems with two 1-variable inequalities in them. It will again be two arrows, but this time we won't need them to overlap. That means that there is no solution to this set of three inequalities, which is a perfectly valid answer! Mathematics. succeed. Log in or sign up to add this lesson to a Custom Course. This straightforward worksheet is for students to practise using number lines and set notation interchangeably. How to write a solution set using Set Builder notation. Set Notation and Interval Notation Solve Linear Inequalities Compound Inequalities Absolute Value Equations Absolute Value Inequalities Arithmetic Sequences & College Algebra in Context Introduction to Arithmetic Sequences Summation Notation Finding the Sum of an Arithmetic Sequence Distance, Rate, and Time Determine an Equation in Context Solving Problems … For example, a 92 is greater than or equal to 80, but it is not less than 90. Curly Braces: { } 2. | {{course.flashcardSetCount}} first two years of college and save thousands off your degree. greater than less than t greater than or equal to d less than or equal to … The closing parenthesis on the other end, ), indicates that 90 is not included in the solution and is the same as saying less than. 4` The set of all real numbers is written f ,f. Linear Inequalities and Absolute Value Inequalities There are 4 types of inequalities: ! For example, the answer to our 'and' compound inequality could be expressed using interval notation like this: [80,90). 's' : ''}}. We get this picture by graphing one inequality at a time and then seeing where the two graphs overlap. This also changes our graph from a single dot with an arrow going forever in one direction, to two dots with a line segment connecting them. Quiz & Worksheet - Set Notation, Compound Inequalities & Systems of Inequalities, Over 83,000 lessons in all major subjects, {{courseNav.course.mDynamicIntFields.lessonCount}}, How to Graph 1- and 2-Variable Inequalities, How to Solve and Graph an Absolute Value Inequality, Solving and Graphing Absolute Value Inequalities: Practice Problems, Biological and Biomedical How to write a solution set using Set Builder notation. We can start by graphing x ≥ 80. This is read as `x` such that `x` is greater than > 5. (18.00) O c.(-0, a Od (-0, i A compound inequality where only one condition must be satisfied is called an 'or' compound inequality and will have a graph with two intervals that looks like this: Before we move on, let's talk about two mathematical notations commonly used to describe the solution sets of compound inequalities. This notation is especially compact and used more often than set notation for expressing solution sets of compound inequalities. The first set describes all integers that are 5 or greater. To be neat, the smaller number should be on the left, and the larger on the right. Answers are provided. We would begin by graphing the first inequality, y > x + 1, on our coordinate plane, getting this. \frac{(x + 6)(x - 4)}{x - 1} \geq 0, solve the given inequalities. Solve the inequality. All other trademarks and copyrights are the property of their respective owners. Explain why we do not use a bracket in interval notation when infinity is an endpoint. }\) As with equations, we should check solutions to catch both human mistakes as well as for possible extraneous solutions (numbers which were possible solutions according to algebra, but which actually do not solve the inequality). Set Notation . Write the solution set in interval notation. Notation plays an important role in mathematics. Less Than Or Equal To. You will notice that the numbers and symbols in interval notation are written in the same order as a number line. Create an account to start this course today. To solve your inequality using the Inequality Calculator, type in your inequality like x+7>9. We put a closed circle at 80 and draw an arrow going to the right to indicate that the answer could be any number 80 or larger. Compound inequalities involving the word “and” require the intersection of the solution sets for each inequality. It only has to satisfy one of the conditions. Algebra. Share an example of a set described using both systems. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. Edit. You can test out of the So let's swap them over (and make sure the inequalities still point correctly): 1 < t 2 < 2 Just like we can have multiple 1-variable inequalities in a single problem, we can have multiple 2-variable inequalities in a single problem as well. In set notation this interval is represented as ^x x! Check out our iOS app: tons of questions to help you practice for your GCSE maths. In set notation this interval is represented as ^x x! If an answer must satisfy both inequalities, it is called an 'and' compound inequality, but if satisfying one of the inequalities is enough to be a solution, then it is called an 'or' compound inequality. Explain why we do not use a bracket in interval notation when infinity is an endpoint. -2(7y - 7) + y > 2y- (-5 + y) Select one: O a(,00) Ob. They both work. 2077 plays. credit-by-exam regardless of age or education level. But it's sometimes going to be the case that we want to be more specific than these last two examples. The solution set is all values of x, such that x is greater than 30, and less than 45. We could then graph the second inequality, y ≤ -x + 5 directly on top of it to get this. just create an account. With this convention, sets are built with parentheses or brackets, each having a distinct meaning.The solutions to [latex]x\geq 4[/latex] are represented as [latex]\left[4,\infty … Set Notation Students will now be required to represent solutions to inequalities using set notation. These unique features make Virtual Nerd a viable alternative to private tutoring. Express the solution set for this compound inequality using set notation. For example: `{x: x > 5}`. study Write the inequality in interval notation. In this lesson, we'll explore the conditions of compound inequalities and learn how to express them using set notation and interval notation. Therefore, it's not a B. Interval notation is a common way to express the solution set to an inequality, and it’s important because it’s how you express solution sets in calculus. The OCR specification gives us two examples of set notation: It doesn't matter that it isn't also greater than 90. Free inequality calculator - solve linear, quadratic and absolute value inequalities step-by-step This website uses cookies to ensure you get the best experience. The various types of numerical statements are noted below. courses that prepare you to earn Integers in both sets are 5, 6, 7 and 8. (−6,∞) ( - 6, ∞) Enter YOUR Problem. Inequalities can be shown using set notation: {`x`: inequality} where `x:` indicates the variable being described and inequality is written as an inequality, normally in its simplest form. With this convention, sets are built with parentheses or brackets, each having a distinct meaning. For example, what if we were asked to find the area of the graph where both of the following inequalities were true? 9th grade . The notation a > b means that a is greater than b. Another commonly used, and arguably the most concise, method for describing inequalities and solutions to inequalities is called interval notation. flashcard sets, {{courseNav.course.topics.length}} chapters | Which integers are described by this set description? You might see a colon used instead of the vertical line sometimes, but they mean the exact same thing. Let's expand our previous example by adding a third inequality: y > -2x + 50. Research and discuss the different compound inequalities, particularly unions and intersections. To be neat, the smaller number should be on the left, and the larger on the right. Usually, you'll see it when you learn about solving inequalities, because for some reason saying "x < 3" isn't good enough, so instead they'll want you to phrase the answer as "the solution set is { x | x is a real number and x < 3 }". The first set says that anything from 0 up to, but not including 80, is not a B, and the last tells us that anything from 90 to 100 is also not a B. If we were to write the solution set to our 'and' compound inequality in set notation, it would look something like this: What this literally says is that the solution set is all values of x, such that x is greater than or equal to 80 and less than 90. In the previous examples, we used inequalities and lists to describe the domain of functions. greater than less than t greater than or equal to d less than or equal to … The first is called set notation. In this case, for a number, x, to be part of the solution, both conditions must be satisfied. The solution to in set builder notation is _____ To write the inequality in standard form, subtract both sides … This means that our graph is a little bit different as well. As the question states - it's just a different notation to express the same thing. The answer is a finite number of points, written in brackets; for example, {1, 2, 3}.This is the set containing only the elements 1, 2, and 3.But how do we pick a solution set from all the real numbers? 4 years ago. Getting less than 80 is one way to not get a B, but getting 90 or above is another way. Inclusive inequalities with the “or equal to” component are indicated with a closed dot on the number line and with a square bracket using interval notation. Now, instead of having to satisfy both conditions like before, the answer can satisfy either and still be okay. Thanks for contributing an answer to Mathematics Stack Exchange! Visit the Math 101: College Algebra page to learn more. Using set-builder notation, we write the solution set as \(\{x\mid x\leq-6\}\text{. But because we are multiplying by a negative number, the inequalities will change direction ... read Solving Inequalities to see why. So, the lowest value for the inequality is placed on the left side in each set of parentheses or brackets. How do you solve compound inequalities with or? But we can also have what are called 'or' compound inequalities. Type = for "less than or equal to". A more complex inequality would be shown as `{x: -5 < x < 5}`. Set Notation Set notations are used to express solutions to 1-variable inequalities. 4` The set of all real numbers is written f ,f. Linear Inequalities and Absolute Value Inequalities There are 4 types of inequalities: ! QUIZ NEW SUPER DRAFT. Try refreshing the page, or contact customer support. imaginable degree, area of The Next Campus Rockstar: a Math Student? The first example was a 1-variable inequality because the only topic being discussed was the one test score, while the second was a 2-variable inequality because there were video games and plane tickets involved. If an inequality has one or more variables in it, a solution of that inequality is any set of values that can replace the variables to produce a true statement. Anyone can earn Save. When this happens, it's called a system of inequalities. The colon means such that. You can use interval notation to express where a set of solutions begins and where it ends. How do you graph a system of linear inequalities? The solution set of an 'or' compound inequality is written in the same way, but with the word 'or' used instead of 'and': This says that the solution set is all values of x, such that x is less than 80 or greater than or equal to 90. This video introduces how to read and write interval and set notation. x > −6 x > - 6. 2 > t 2 > 1 . Services. Working Scholars® Bringing Tuition-Free College to the Community, Explain the difference between an 'and' compound equality and an 'or' compound inequality, Write a compound inequality in set or interval notation, Identify the solutions for a system of inequalities. Share. What is the definition of a compound inequality? Solve the inequality. Let's look at some examples of how to write inequalities in interval notation. Get access risk-free for 30 days, Strict inequalities without the “or equal to” component are indicated with an open dot on the number line and a parenthesis using interval notation. Copy and Edit. flashcard set{{course.flashcardSetCoun > 1 ? When we change 'greater than 80' into 'between 80 and 90,' we change this single inequality into a compound inequality because it now has two conditions: x ≥ 80 and x < 90. It can be a little bit nicer to read but … Then, we can put a closed circle at 90 and draw our arrow to the right to show that all values greater than or equal to 90 are included. Write the solution in interval notation. For example: `{x: x > 5}`. I will try to help students understand what they are trying to say rather than simply memorizing the symbols that are used in set builder notation. An error occurred trying to load this video. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. Again, we're not worried about where these graphs overlap because satisfying either one of these conditions is enough; they don't have to satisfy both to not be a B. As we can see from the graph, there are several places where the shading for any two of the three inequalities overlaps, but no single area where all three overlap. If we expressed the solution to our previous example of how not to get a B, it would like this: [0, 80) U [90,100]. This straightforward worksheet is for students to practise using number lines and set notation interchangeably. The solution set is the union of each individual solution set. Interval notation is a common way to express the solution set to an inequality, and it’s important because it’s how you express solution sets in calculus. Solve the inequality x2 – x > 12. Expressing the solution to 'or' compound inequalities is a little more complicated because there are two intervals in the solution instead of one. If students struggle, it will most likely be with question #2. To learn more, visit our Earning Credit Page. The solution set of an inequality can also be described by using set-builder notation . These are the values that solve at least one of the given inequalities. maxstraub. Free inequality calculator - solve linear, quadratic and absolute value inequalities step-by-step This website uses cookies to ensure you get the best experience. How to solve basic compound inequalities. For example, if, instead, we were describing the different ways I could get something other than a B, we would want to say that I could get less than an 80 or greater than or equal to 90. For example, a 72% is less than 80, so it's not a B. Report your solutions using interval notation a) \left | x+1 \right | - \left | x-1 \right |+\left | x \right |-\left | 2x-6 \right |greater-than or equal to 2x-4 b) \le. Study.com has thousands of articles about every By using this website, you agree to our Cookie Policy. The colon means such that. Interval Notation Examples. Play this game to review Algebra I. This means the only part of the graph we want is where they overlap, and what we end up with is a line connecting our two points. Did you know… We have over 220 college Set Notation . 68% average accuracy. Most pre-calculus books and some pre-calculus teachers now require all sets to be written in interval notation. Or more 2-variable inequalities the conditions of compound inequalities involving the word “ or ” the... Involving the word “ and ” require the intersection of the solution to this set of inequalities... A Custom Course its simplest form in set notation, you should be on right... Some pre-calculus teachers now require all sets to be part of the graph where both the... Info you need to find the area of the vertical line symbol, U in! That we want to know if there is no solution to this set of an inequality can also described. To add this lesson to a Custom Course addition to representing solutions on number lines and set notation interchangeably -. On top of it to get this picture by graphing one inequality at a time the symbol U... Are represented as ^x x this video introduces how to write inequalities in interval notation and set Builder notation:... Are multiplying by a negative number, the answer can satisfy either and still be okay a alternative! -5 + y > x + 1, on our coordinate plane, getting this the that. The left, and the larger on the left, and has a master degree... For `` less than 80 is one way to not get a.... Put an open circle at 80 and draw our arrow to the student understanding! And ” require us to solve basic compound inequalities as ` { x: -5 < x < 5 `! Indicates that 80 is one way to not get a b, but getting 90 or above is another.! Cookie Policy for `` less than or equal to 80, so it 's called a system of inequalities working. The most concise, method for describing inequalities and solutions to 1-variable inequalities inequalities: set.! Be expressed using interval notation times when a system of inequalities are free to take whatever path through the best! By graphing the first number is the space where they are both true, x to! Log in or sign up to add this lesson to a Custom Course the to. Of either inequality credit-by-exam regardless of age or education level whatever path through the best. Then seeing where the two graphs overlap set using set Builder notation for (... You will notice that the solution and is equivalent to saying greater or. Add this lesson to a Custom Course 's talk about two mathematical notations commonly,... Answer can satisfy either and still be okay more specific than these last two examples master 's in! You look for a characteristic that identifies the elements of your set info you need to the... Set of solutions for which all three inequalities are problems with two 1-variable inequalities written with a instead. Notation are written in the new maths GCSE specification states that students will have to represent using... Equal to … how to solve it on your own inequalities is called set notationto express solutions to are... Resources for teaching topics in the solution sets of compound inequalities is called set notationto express to! Log in or sign up to add this lesson, you look for a,. Anything to the left showing that all values less than 80 are included the solution set parentheses! It on your own find the right describing inequalities and solutions to 1-variable.. College algebra page to learn more ` { x: -5 < x < set notation inequalities } ` solutions inequalities... Set Builder notation you should be on the left side in each of! > 2y- ( -5 + y ) Select one: O a (,00 ) Ob available... How this adds anything to the student 's understanding, I do know... To this set of an inequality can also have what are called 'or ' inequality. Write interval and set Builder notation for inequalities ( new GCSE ) new! New maths GCSE specification states that students will have to remember that the numbers and symbols in interval.... Are free to take whatever path through the material best serves their needs but we. Going to be neat, the smaller number should be on the left, and the second inequality, >! When this happens, it 's not a b, but this time wo! Is written with a bar instead of one using set-builder notation than less than 80 included! Will change direction... read Solving inequalities to see why steps to help learn! Is n't also greater than less than 90 the new GCSE are available on my resourceaholic.com. 80, so it 's called a system of inequalities are true identifies the elements of your.... By passing quizzes and exams will notice that the numbers and symbols in interval notation is. Inequalities step-by-step this website uses cookies to ensure you get the best experience practice tests, quizzes and. Using set Builder notation second notation we can put an open circle at and... Case that we want to attend yet to learn more best experience both! ' compound inequalities - it 's not a b GCSE ) the maths! Interval notation are written in interval notation when infinity is an endpoint it! Out of the solution is the union of each individual solution set using set notation.! Other answers,00 ) Ob look for a characteristic that identifies the elements of your.! Create an account copyrights are the values that solve at least one of the set... Introduces how to write inequalities in interval set notation inequalities might see a colon {. Be more specific than these last two examples picture by graphing one inequality at a time and then seeing the! 'S degree in education or more 2-variable inequalities example: ` { x: >. You learn how to read and write interval and set Builder notation a! Be the case that we want to be neat, the smaller number should be able:! Through the material best serves their needs the larger on the right < 5 } ` school. A Custom Course want to attend yet have what are called 'or ' compound involving... To preview related courses: the first number is the space where are. Right school are noted below commonly used to describe the solution set from a replacement.... The given inequalities complex inequality would be shown as ` { x: x > 5 }.... Numerical statement ^x x solution to this set of solutions for which all three inequalities, particularly unions intersections... Website, you should be able to: to unlock this lesson to a Custom Course high school and...: college algebra page to learn more, visit our Earning Credit page.. Integers in both sets are 5, 6, 7 and 8 what college you want to written. Another set notation inequalities up to add this lesson, you agree to our Cookie Policy can out... That we want to attend yet a (,00 ) Ob compound inequalities involving the word or... College and save thousands off your degree in or sign up to add this lesson, we write solution! Conditions of compound inequalities: set notation interchangeably practice for your GCSE maths solve linear quadratic... So it 's not a b, but getting 90 or above another! Select a subject to preview related courses set notation inequalities the first inequality, y ≤ -x 5! With set notation are known as strict inequalities, meaning that a is greater than.., both conditions like before, the answer can satisfy either and still be okay characteristic that identifies elements! Do not use a bracket in interval notation described using both systems number lines and graphs if we asked. Inequalities to see why we 'll explore the conditions for describing inequalities and solutions to 1-variable inequalities the value! Our previous example by adding a third inequality: y > x + 1, on coordinate! A third inequality: y > 2y- ( -5 + y ) Select one: a... Question # 2 through the material best serves their needs lowest value for the solver. Again be two arrows, but they mean the exact same thing from! For example: ` { x: x > 5 ` } simplest... Values less than or equal to b be sure to answer the question.Provide details and your. Need to find the right an answer to our 'and ' compound inequalities is a valid... Students set notation inequalities, it 's just a different notation to express solutions to 1-variable inequalities is for to! Could then graph the second inequality, y ≤ -x + 5 on. Called interval notation like this: [ 80,90 ) greater than or strictly greater or! Of questions to help you practice for your GCSE maths set from a replacement set the lower bound and... Will most likely be with question # 2 x¦ x > 5 an open circle at 80 draw! 4 > 0 ` in its simplest form in set notation arrow to the student 's understanding I... Student 's understanding, I do n't know perfectly valid answer integers that are 5, 6, ). And some pre-calculus teachers now require all sets to be part of the vertical line sometimes but! Be on the left, and has a master 's degree in.... Each set of an inequality can also be described by using set notation inequalities website, you to... Or equal to a characteristic that identifies the elements of your set and the second inequality, y ≤ +... - 4 > 0 ` in its simplest form in set notation is especially compact used...