Question

solve the inequality |2x + 1| > 7
a {x|x < -4 or x > 3}

b {x|x < -4}

c {x|x > 3}

d {x|-4 < x < 3}

Explanation:

Step1: Apply absolute value rule

For $|A| > B$, $A > B$ or $A < -B$. So:
$2x+1 > 7$ or $2x+1 < -7$

Step2: Solve first inequality

Subtract 1, then divide by 2:
$2x > 7-1$
$2x > 6$
$x > 3$

Step3: Solve second inequality

Subtract 1, then divide by 2:
$2x < -7-1$
$2x < -8$
$x < -4$

Answer:

A. $\{x|x < -4 \text{ or } x > 3\}$