GRE Math : Inequalities

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Example Question #6 : How To Find The Solution To An Inequality With Addition

What values of make the statement $\left |5x-9 \right |\geq6$ true?

Possible Answers:

$x\geq5,x\leq \frac{1}{5}$

$x\geq6,x\leq \frac{1}{3}$

$x\geq4,x\leq -\frac{1}{2}$

$x\geq15,x\leq \frac{2}{5}$

$x\geq3, x\leq \frac{3}{5}$

Correct answer:

$x\geq3, x\leq \frac{3}{5}$

Explanation:

First, solve the inequality $5x-9 \geq6$ :

$5x-9 \geq6$

$5x\geq15$

$x\geq3$

Since we are dealing with absolute value, $5x-9\leq-6$ must also be true; therefore:

$5x-9\leq-6$

$5x\leq3$

$x\leq \frac{3}{5}$

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GRE Math : Inequalities

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #6 : How To Find The Solution To An Inequality With Addition

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