union and intersection of inequalities calculator

Math can be daunting for some, but with a little practice it can be conquered! 20% Continue to start your free trial. The intersection of two sets, denoted AB ("A intersect B") is the set of all members contained in bothA and B. Consider the intersection of two streetsthe part where the streets overlapbelongs to both streets. There are no numbers that make both inequalities true. How many hcf will he be allowed to use if he wants his usage to stay in the normal range? O LINEAR EQUATIONS AND INEQUALITIES Union and intersection of intervals and C are sets of real numbers defined as follows. If you don't see it, please check your spam folder. Dont have an account? To begin with, our tool (like any other calculator) prefers numbers. Math is a challenging subject for many students, but with practice and persistence, anyone can learn to figure out complex equations. Universal set. Graph the solution and write the solution in interval notation. Thanks for creating a SparkNotes account! The math intersection sign is , i.e., we read AB as A intersection B or the intersection of A and B. Alright, we've defined the union and intersection formally, but let's maybe spare a few sentences to translate them to everyday language. (one code per order). To find the solution of an "and" compound inequality, we look at the graphs of each inequality and then find the numbers that belong to both graphswhere the graphs overlap. How to Find the Intersection of Inequalities Kathryn Hernandez 6.13K subscribers Subscribe 11K views 4 years ago This video covers one example on how to find the intersection when given two. It is the overlap, or intersection, of the solutions for each inequality. Homework Support Online is a great resource for students who need help with their homework. Inequality Calculator Set Calculator - Union, Intersection, and Difference of Sets Use this calculator to calculate the union, intersection, or difference between two sets. Explanation Check SOLVE A COMPOUND INEQUALITY WITH "OR." The procedure to use the compound inequality calculator is as follows: Step 1: Enter two inequality equations in the respective input field Step 2: Now click the button "Solve" to get the inequality Step 3: Finally, the inequality equation with the number line will be displayed in the new window What is Meant by Compound Inequality? Every point on the dark line is a member of the set {x : 0x < 4}. After checking with the weight loss calculator and taking special care of their diet, they decide to take up a physical activity. Solve the compound inequality. Union of Sets, In our first example, AB = {0, 1, 2, 3, 4, 5, 6}: A compound inequality is made up of two inequalities connected by the word and or the word or. For example, the following are compound inequalities. Thus, {x : x < 7orx11} = {x : x < 7} {x : x11}. It is really great for all math sometimes it can't quite figure it out but if you just put it in a different way you'll get it eventually. Solve \(4\leq 3x7<8\). It will also, Set Calculator - Union, Intersection, and Difference of Sets Use this calculator to calculate the union, intersection, or difference between two sets. Use up and down arrows to review and enter to select. Subscribe now. Intersection of sets: The intersection of two sets A and B, denoted by A B, is the set of all elements which are common to both A and B. We can graph the union of two inequalities on the number line. In math, we call this property the commutativity of the union and intersection of sets. We guarantee that your essay will be original. Start by copy-pasting your two sets into. This is an amazing app you can solve any type of problem and it recognizes all steps to solve the problem and it's a fast working app and ads aren't annoying for once. Union of set A and set B. Report an issue. To do this, How to find the area of a square with the diagonal, How to write domains in interval notation, Find all real zeros of the polynomial function. When we see a statement like "0x < 4", also written as "0x and x < 4", or as {x : 0x < 4}, the compound inequality or the word and denotes the intersection of the two sets of numbers which satisfy each inequality. Add the elements from the second set. It will also. Just as the United States is the union of all of the 50 states, the solution will be the union of all the numbers that make either inequality true. To determine what the math problem is, you will need to look at the given information and figure out what is being asked. This helps my granddaughter so much she gets anciety attacks saying shes going to fail but this really helped her with her math and social studies. It's free to sign up and. Then graph the numbers that make either inequality true. To, Calculators; Critical Value Tables; Glossary; Posted on September 11, 2018 August 23, 2021 by Zach. Graph system of inequalities and find intersections step-by-step. It is equivalent to \(a3\) and \(x\leq 2\), we graph each inequality. Get the latest news and updates on the go with the 24/7 News app. Members will be prompted to log in or create an account to redeem their group membership. Graph the solution and write the solution in interval notation: \(\frac{1}{4}x3\geq 1\) and \(3(x2)\geq 2\). On the other hand, Mark enjoys dancing, tennis, soccer, and cycling. Solve the compound inequality. Welcome to Omni's union and intersection calculator, where we'll learn how to find AB and AB, i.e., A union B and A intersection B. You can view our. Since A and B have no members in common, AB = (the null set). Then graph the numbers that make. Graph the solution and write the solution in interval notation. This calculator will compute the probability of event A or event B occurring (i.e., the union probability for A and B), given the probability of event A, the probability of event B, and. To solve a double inequality we perform the same operation on all three parts of the double inequality with the goal of isolating the variable in the center. Operations on Sets Calculator show help examples Input Set A: { } Input Set B: { } Choose what to compute: Union of sets A and B Intersection of sets A and B The union of sets A and B gathers all elements that fall in A, in B, or in both. Math Solver. Want 100 or more? In other words, for any two sets A and B, we have: Check out 37 similar algebra calculators , Union and intersection of sets and their symbols, Example: using the union and intersection calculator, the distributive property of multiplication over addition, graphing inequalities on a number line calculator. To solve a math equation, you need to decide what operation to perform on each side of the equation. The number of hcf he can use and stay in the normal usage billing range. It is very reliable with most of the time giving me correct results, save time a lot. Mathematics is the study of numbers, shapes, and patterns. Graph the solution and write the solution in interval notation: \(\frac{3}{5}x7\leq 1\) or \(\frac{1}{3}(x+6)\geq 2\). Then, according to the explanation above: Furthermore, observe that it doesn't really matter in what order we take the sets: AB is the same as BA, and AB is the same as BA. Get Annual Plans at a discount when you buy 2 or more! The inequality solver will then show you the steps to help you learn how to solve it on your own. answer choices. The value 2 satisfies the statement, but the value -3 does not, and the value 5 does not. Youve successfully purchased a group discount. We offer fast professional tutoring services to help improve your grades. T = multiples of 2 in the universal set = {2, 4, 6, 8, 10} F = multiples of 4 in the universal set = {4, 8} In a Venn diagram, we would represent the universal set with a large rectangle and we. If you don't see it, please check your spam folder. Sometimes we have a compound inequality that can be written more concisely. We offer immediate delivery on all orders placed before 3pm. \[\text{Other forms:} \quad \begin{array} {lllll} {ax>b} &{\text{is equivalent to }} &{a>x} &{\text{and}} &{x>b} \\ {a\geq x\geq b} &{\text{is equivalent to }} &{a\geq x} &{\text{and}} &{x\geq b} \\ \end{array} \nonumber\]. This calculator is an online tool to find find union, intersection, difference and Cartesian product of two sets. Q. To determine a mathematic question, first consider what you are trying to solve, and then choose the best equation or formula to use. One instrument that can be used is Union and intersection of inequalities calculator. x^ {\msquare}. Calculators; Critical Value Tables; Glossary; Posted on September 11, 2018 August 23, 2021 by Zach. Union-Intersection-Disjoint Set Calculator Intersection of set, Union of Sets, Disjoint of set, Definition, Formulas, Calculator Union-Intersection-Disjoint of set Calculator An online Union and Intersection and Disjoint of sets calculation. L 2 = {11, 011, 101, 110, 0011, 1100, } L = L 1 and L 2 = L 1 L 2 Sets Intersect Calculator - Symbolab So essentially, the desired output would be as follows: In this case: intersection = 3.2773 (with-1-tyre-n) and union = 29.3546. where we get a score by dividing the union by the intersection: score (intersection)/ score (union) So, from this . Step 3: Finally, the expanded form and solution of the given rational inequality will be displayed in the new window. SparkNotes PLUS To find the union and intersection of two sets, you need to: List all elements from the first set. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Another way to graph the solution of \(1\leq x<5\) is to graph both the solution of \(x\geq 1\) and the solution of \(x<5\). Renew your subscription to regain access to all of our exclusive, ad-free study tools. It will also generate a step by step explanation for each operation. However, new ones appear once you begin inputting the values. To solve a math equation, you need to decide what operation to perform on each side of the equation. Every point on the dark line is a member of the set {x : x < 7orx11}. Example 3. The usage is measured in the number of hundred cubic feet (hcf) the property owner uses. We then look for where the graphs overlap. Situations in the real world also involve compound inequalities. Once you know what the problem is, you can solve it using the given information. Thus, A B = {x : x A or x B}. Groups Cheat Sheets . Get Annual Plans at a discount when you buy 2 or more! Solve math equation The two forms are equivalent. Did you know you can highlight text to take a note? It will also generate a step by step explanation for each operation. For instance, even though we've defined the union and intersection of only two sets, we can easily extend it to more. for a group? As such, it's a subset of each of them. Let's use Omni Calculator's union and intersection calculator to find what the couple may like. \[\begin{array} {lll} {x+3>4} &{\text{and}} &{4x5\leq 3} \\ {2(y+1)<0} &{\text{or}} &{y5\geq 2} \\ \end{array} \nonumber\], A compound inequality is made up of two inequalities connected by the word and or the word or.. Use this calculator to calculate the union, intersection, or difference between two sets. Please wait while we process your payment. Union of Inequalities It's pretty cool it does give the answers but now the work that sucks you have to put premium in order to get the full work. For every element, check if it's in the sets: The union gathers those that appear in at least one; and The intersection gathers those that appear in both. For instance, the intersection of two sets with one entirely contained in the other is equal to the smaller one. $24.99 Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. By the end of this section, you will be able to: Before you get started, take this readiness quiz. $24.99 To learn more about representing numbers on a line, check out the graphing inequalities on a number line calculator! To solve a math problem, you need to figure out what information you have. Probability of event A: P(A), Expert teachers will give you an answer in real-time. Next, restate the problem in one sentence to make it easy to translate into a compound inequality. When we are putting the x2+6x+9>0 in the compound inequalities calculator, we find the roots x>-3 and x<3. To find the union and intersection of two sets, you need to: List all elements from the first set. To solve a compound inequality with the word and, we look for all numbers that make both inequalities true. We would then find the numbers that make both inequalities true as we did in previous examples. Very easy to use and it even shows the solution, thanks, This app, very useful and is way better than photo math i like how you were able to choose which type of problem you needed to do, easy way to check homework answers to make sure they are correct, and the student is on the right path. There, we'll see: However, before we reveal the answer, let's find it ourselves. Lets start with the compound inequalities with and. Our solution will be the numbers that are solutions to both inequalities known as the intersection of the two inequalities. Dont have an account? graphing calculator. In our first example, AB = {2, 4, 6}: To do this. The bill for Normal Usage would be between or equal to $57.06 and $171.02. Check the subset calculator to learn more about them! Then darken the line which appears in the graph of both inequalities. Your subscription will continue automatically once the free trial period is over. We can see that the numbers between \(3\) and \(2\) are shaded on both of the first two graphs. TO CANCEL YOUR SUBSCRIPTION AND AVOID BEING CHARGED, YOU MUST CANCEL BEFORE THE END OF THE FREE TRIAL PERIOD. On the other hand, the intersection gathers all the elements common to each and every one of the sets. 2.9: Solve Compound Inequalities - Union, Intersection is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts. As such, it's always smaller than or equal to either of the two - i.e., it's a subset of both. Use interval notation to describe sets of numbers as intersections and unions When two inequalities are joined by the word and, the solution of the compound inequality occurs when both inequalities are true at the same time. If you are looking for help with arithmetic, there are many online resources available to support you. on 50-99 accounts. Probability of event A: P(A). We can then graph the solution immediately as we did above. Graph each solution. <p>Intersection of set A and set B</p>. A double inequality is a compound inequality such as \(a9. Last, we will solve the compound inequality. To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement. System of Inequalities Calculator - Symbolab System of Inequalities Calculator Graph system of inequalities and find intersections step-by-step full pad Examples Related Symbolab blog posts High School Math Solutions - Inequalities Calculator, Exponential Inequalities Last post, we talked about how to solve logarithmic inequalities. This calculator is an online tool to find find union, intersection, difference and Cartesian product of two sets. The intersection of two sets is the set containing all elements that belong to both the first and the second set. Solve the compound inequality. Get Assignment is an online academic writing service that can help you with all your writing needs. During the winter, a property owner will pay $24.72 plus $1.54 per hcf for Normal Usage. SparkNotes Plus subscription is $4.99/month or $24.99/year as selected above. It is used in everyday life, from counting to measuring to more complex calculations. To figure out a mathematic equation, you need to use your brain power and problem-solving skills. Graph the solution and write the solution in interval notation: \(12x\leq 3\) or \(7+3x\leq 4\). Union of Inequalities When we see a statement like " x < 7 or x11 ", written in set notation as {x : x < 7orx11}, the word or denotes the union of the two sets of numbers which satisfy each inequality. The inequality solver will then show you the steps to help you learn how to solve it on your own. The easiest way to write the union of two sets is to write all the members in the first set, and then write all the members in the second set that haven't been written yet: It's just a matter of choosing the right one. If you want to enhance your academic performance, start by setting realistic goals and working towards them diligently. Solve the compound inequality. Inequalities Calculator Set Calculator - Union, Intersection, and Difference of Sets Use this calculator to calculate the union, intersection, or difference between two sets. No matter what question you have, our expert teachers will have an answer for you in no time. You'll be billed after your free trial ends. Solve \(\frac{2}{3}x4\leq 3\) or \(\frac{1}{4}(x+8)\geq 1\). on 2-49 accounts, Save 30% Solve \(53x\leq 1\) or \(8+2x\leq 5\). Recall the problem solving strategies are to first read the problem and make sure all the words are understood. Obviously, apart from learning the symbols for set operations, we'll formally define the union and intersection of sets to see what the difference is. Youve successfully purchased a group discount. We solve each inequality separately and then consider the two solutions. Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. That'll trigger two sections underneath: one for set A and one for set B. For example, the union of two sets with one entirely contained in the other is equal to the larger one. The similarities may help you wonder if we have here an equivalent of another arithmetic law: the distributive property of multiplication over addition. Renews January 24, 2023 Union of set Intersection of set Disjoint of set Definition Looking for someone to help with your homework? In total, you can have sets with up to ten elements each.). There are different rates for Conservation Usage, Normal Usage and Excessive Usage. They are graphic representations using circles or ellipses for each of the sets, with the shapes intersecting to show which elements are common and which are not. We're sorry, SparkNotes Plus isn't available in your country. Thus, {x : x < 7orx11} = {x : x < 7}{x : x11}. We can provide expert homework writing help on any subject. To write the solution in interval notation, we will often use the union symbol, , to show the union of the solutions shown in the graphs. In fact, this notation makes sense because both operations satisfy the associative property: At this point, you may feel that the union and intersection of sets are quite similar to the two basic arithmetic operations: addition and multiplication. 9j gt 36 q lt 5 or q gt 9 Compound Inequality such as 2 lt b lt 5 x lt 3 Reverse Interval notation to Inequality Solver Set Union Intersection and Relative . Mathematical equations are used to solve problems or to describe relationships between variables. On the one hand, the union gathers all the elements occurring in at least one of the sets. To find the solution of the compound inequality, we look at the graphs of each inequality, find the numbers that belong to either graph and put all those numbers together. Union and intersection probability calculator. You may cancel your subscription on your Subscription and Billing page or contact Customer Support at custserv@bn.com. Thus, XY has 5 + 5 - 3 = 7 members. This is the set of values which satisfy eitherx union of two inequalities on the number line. Start by copy-pasting your two sets into 244 Math Experts 9.7/10 Ratings 63693+ Completed orders Get Homework Help In other words, for any sets A, B, and C, we have: Yes. Graph the solution and write the solution in interval notation: \(\frac{1}{5}x5\geq 3\) and \(4(x1)\geq 2\). For that, we select 2 under "Number of sets" (since we have two people) and "individual entries" under "Input form" (since we'll list the activities one by one). Purchasing To find the solution of the compound inequality, we look at the graphs of each inequality, find the numbers that belong to either graph and put all those numbers together. This problem is a great way to practice your math skills. Probability of event A: P(A), How to find the absolute maximum and minimum of a function. to start your free trial of SparkNotes Plus. To write the solution. To determine what the math problem is, you will need to look at the given information and figure out what is being asked. Save over 50% with a SparkNotes PLUS Annual Plan! We're sorry, SparkNotes Plus isn't available in your country. Intersection of A and B XY = { -4, 3, 11} Due to the drought in California, many communities have tiered water rates. We can think of the intersection of two sets as the overlap in the Venn diagram: You'll also receive an email with the link. Your subscription will continue automatically once the free trial period is over. Very helpful! Given two any real intervals, its union is a set that consists of all the elements that belong to the first interval and all the elements that belong to the second one. Intersection of set A and set B. For that, below, we've defined the union and intersection again, but using everyday language. What is XY if X = { -4, 3, 2, 11, -6} and Y = {3, 6, 11, -4, 5}? We can graph the intersection of two inequalities on the number line. Your group members can use the joining link below to redeem their group membership. The free trial period is the first 7 days of your subscription. Lastly, let us mention that the comparison of union vs. intersection is best portrayed by so-called Venn diagrams. Math is all about finding the right answer, and sometimes that means deciding which equation to use. Set Calculator - Union, Intersection, and Difference of Sets Use this calculator to calculate the union, intersection, or difference between two sets. Looking for a little help with your homework? Looking for a little help with your math homework? The union of two sets is the set containing all elements that belong to at least one of the initial sets. wow how to get to blasted lands from stormwind . Thanks for creating a SparkNotes account! The absolute BEST math app ever made. Therefore, let us translate all the activities listed above to consecutive integers: Looking at the union and intersection calculator, we see that first, we need to tell the tool what we're dealing with. Intersection of {1, 2, 3, 4, 5, 6} and {0, 2, 4, 6} This calculator is an online tool to find find union, intersection, difference and Cartesian. During the summer, a property owner will pay $24.72 plus $1.32 per hcf for Conservation Usage. Solve \(6x3<9\) and \(2x+7\geq 3\). I can't tell you how much this app had saved me from making a mistake. Graph the solution and write the solution in interval notation: \(5\leq 4x1<7\). The Best Union and intersection of intervals solver. This is the set of values which satisfy both0xandx < 4. The shaded part of this image shows the ______. Welcome to Omni Calculator's union and intersection calculator, where we'll learn how to find AB and AB, i.e., A union B and A intersection B. Sometimes the two inequalities will overlap. Suppose that Amy and Mark want to lose some weight after the pandemic lockdowns and restrictions. This takes us to set operations. Check out our solutions for all your homework help needs! Graph the solution and write the solution in interval notation. Welcome to Omni's union and intersection calculator, where we'll learn how to find AB and AB, i.e., A union B and A intersection B. Example 3: What is XY if X = { -4, 3, 2, 11, -6} and Y = {3, 6, 11, -4, 5}? for a customized plan. Start by copy-pasting your two sets into, This is the set of values which satisfy eitherx union of two inequalities on the number line. Union and Intersection Calculator This calculator will compute the probability of event A or event B occurring (i.e., the union probability for A and B), given the probability of event A, the probability of event B, and Deal with math tasks One way to think about math problems is to consider them as puzzles. On the other hand, the intersection of sets A and B gathers elements common to both, i.e., all that fall both in A and in B. To do this, This calculator is an online tool to find find union, intersection, difference and Cartesian product of two sets. To solve a math equation, you need to find the value of the variable that makes the equation true. SparkNotes PLUS Renews January 25, 2023 Wed love to have you back! Solve the compound inequality. Operations on sets calculator. Graph the solution and write the solution in interval notation. Use up and down arrows to review and enter to select. One way to think about math problems is to consider them as puzzles. Solve the compound inequality. Cross out any repetitions (i.e., leave one copy of each). By signing up you agree to our terms and privacy policy. You cam type any equation be it quadratic, algebraic whatsoever and it will bring out the answer step by step Thank you very much, this app helped me get through 3 DAYS STRAIGHT worth of a math class & it pulled through. 2: Solving Linear Equations, Formulas, and Inequalities, Math 084: Intermediate Algebra Foundations for Soc Sci, Lib Arts and Gen Ed, { "2.9E:_Exercises" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "2.01:_Prelude_to_Solving_Linear_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.02:_Use_a_General_Strategy_to_Solve_Linear_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.03:_Use_a_Problem_Solving_Strategy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.04:_Solve_a_Formula_for_a_Specific_Variable" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.05:__The_Pythagorean_Theorem" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.06:_Solve_Mixture_and_Uniform_Motion_Applications_(optional_practice)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.07:_Solve_Applications_with_Linear_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.08:_Solve_Linear_Inequalities_-_Algebra_Emphasis" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.09:_Solve_Compound_Inequalities_-_Union_Intersection" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.10:_Graphs_of_Linear_Inequalities_in_Two_Variables_(optional_challenge_practice)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.11:_Solve_Absolute_Value_Inequalities_(optional_challenge_practice)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Introduction_to_Graphing_-_By_Hand_and_Calculator" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Solving_Linear_Equations_Formulas_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Graphing_Lines_in_Two_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Rules_of_Exponents_and_Scientific_Notation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 2.9: Solve Compound Inequalities - Union, Intersection, [ "article:topic", "license:ccbyncsa", "showtoc:no", "transcluded:yes", "source[1]-math-17390" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FHighline_College%2FMath_084__Intermediate_Algebra_Foundations_for_Soc_Sci_Lib_Arts_and_GenEd%2F02%253A_Solving_Linear_Equations_Formulas_and_Inequalities%2F2.09%253A_Solve_Compound_Inequalities_-_Union_Intersection, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Solve Applications with Compound Inequalities, status page at https://status.libretexts.org.

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