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Pearson Algebra 2 Common Core, 2011 View details

6. Absolute Value Equations and Inequalities

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Exercise 59 Page 47

Absolute values are always non-negative.

Solution Set: All real numbers.
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Before we can solve this inequality, we need to isolate the absolute value expression using the Properties of Inequality.

-2|x+4|<22

DivNegIneq

Divide by - 2 and flip inequality sign

|x+4|> - 11

All absolute value expressions are greater than or equal to zero. It follows then that any absolute value expression is greater than all negative numbers. |x+4|≥ 0 ⇒ |x+4|>- 11 This means any value of x will satisfy the inequality. Thus, there are infinitely many solutions, and the solution set is the set of all real numbers.