Chapter 9 - Inequalities and Problem Solving - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set - Page 599: 67

all real numbers

Work Step by Step

The absolute value of $x,$ written as $|x|,$ is the distance of $x$ from $0,$ and hence, is always a nonnegative number. Therefore, the left side of the given inequality, $|2y-9|\gt-5 ,$ is always nonnegative. This is always greater than the negative value at the right. Hence, the solution is the set of all real numbers.

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