Question

Solve for $x:$ $|3x+2|\ge 7$

• A. $(-\infty ,-3]\cup [\frac{5}{3},\infty )$
• B. $(-\infty ,-\frac{5}{3}]\cup [3,\infty )$
• C. $(-3,0]\cup [\frac{5}{3},\infty )$
• D. $(-5,-3]\cup [\frac{5}{3},\infty )$

Answer 1

The correct option is A $(-\infty ,-3]\cup [\frac{5}{3},\infty )$

Given $\mid 3x+2\mid \ge 7$

$⟹-7\ge 3x+2\ge 7$

$⟹3x+2\le -7$ (or) $3x+2\ge 7$

$⟹3x\le -7-2$ (or) $3x\ge 7-2$

$⟹x\le \frac{-9}{3}$ (or) $x\ge \frac{5}{3}$

$⟹x\le -3$ (or) $x\ge \frac{5}{3}$

$⟹(-\infty ,-3]\cup [\frac{5}{3},\infty )$