Some of the questions on the TASC Math exam may ask you to solve an inequality. Of course, an inequality won't necessarily involve a 'does not equal' sign; there are actually five symbols that can be classified as inequalities:


Solving an inequality involves following the same steps you use for solving an equation except for one crucial detail: When you multiply or divide by a negative number, you must flip the inequality symbol. Just like with equations, you can still check your answers by substituting them back into the original.

It's important to note that < or > results in an open circle


on a number line because that value is not included as a solution;


The following examples illustrate some of the different types of inequality problems that you may encounter.

Example 1: Linear inequality


Check: You want to pick a value in the solution set. Because your answer is x > 3, you have to pick a value greater than 3. For this example, you use 5.


Example 2: Linear inequality with negative coefficient




Example 3: Does not equal


Check: For this type of problem, you can pick any number except 1/2. So for this example, you can pick 1 to check your solution.


About This Article

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About the book authors:

Stuart Donnelly, PhD, earned his doctorate in mathematics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country. Nicole Hersey, PhD, is a lecturer at the University of Rhode Island, with a dual appointment to the School of Education and the Department of Mathematics. Ron Olson, MA, is an NBCT-certified teacher in Social Studies who teaches AP Government, Civics, and Contemporary World Problems at Clover Park High School in Lakewood, WA. In addition to his 35 years of teaching experience, he works as an AP US History workshop consultant for The College Board and has been the advisor for National Honor Society at his high school. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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