TASC Math Exam—Solving Linear Inequalities

By Stuart Donnelly

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:

TASC_1601

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

TASC_1602

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

TASC_1603

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

Example 1: Linear inequality

TASC_1604

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.

TASC_1605

Example 2: Linear inequality with negative coefficient

TASC_1606

Check:

TASC_1607

Example 3: Does not equal

TASC_1608

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.

TASC_1609