Absolute Value Inequality

Absolute value can also be used in cases of inequality. If the absolute value of an expression is greater than a value, then the expression is either greater than the value or less than the opposite of the value. Let's take a look at an example.

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Consider the example of the absolute value of 2 x plus 6 is greater than 10. The two possible solutions of this problem are 2 x plus 6 is greater than 10 or 2 x plus 6 is less than minus 10.
The inequality has two possible solution sets: 2 x plus 6 is greater than 10 2 x is greater than 4 x is greater than 2 2 x plus 6 is less than minus 10 2 x is less than minus 16 x is less than minus 8
This can be represented on a number line as follows: Number line with values to the left of minus 8 and to the right of 2 selected. Notice that the number line plots the solution of both sets to determine the solution range of this problem.

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