Question

Solve the inequality $3x+2>-16,2x-3\le 11$

• A. $(-6,7)$
• B. $[-6,7)$
• C. $(-6,7]$
• D. $[-6,7]$

Answer 1

Answer: (C)

We have, $3x+2>-16$
$\Rightarrow$ $3x>-16-2$
$\Rightarrow$ $x>\frac{-18}{3}$
$\Rightarrow$ $x>-6$ and $2x-3\le 11$
$\Rightarrow$ $2x\le 11+3\Rightarrow 2x\le 14$
$\Rightarrow$ $x\le \frac{14}{2}\Rightarrow x\le 7$
$\therefore$ Solution of given inequalities is $x\in (-6,7]$