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

The correct option is A

$(-6,7]$

Explanation for the correct option:

Given $3x+2>-16,2x-3\le 11$

Consider the first inequality

$$\begin{gathered} \Rightarrow 3x+2>-16 \\ \Rightarrow 3x>-16-2 \\ \Rightarrow 3x>-18 \\ \Rightarrow x>-\frac{18}{3} \\ \Rightarrow x>-6 \end{gathered}$$

Also consider the second inequality

$$\begin{gathered} \Rightarrow 2x-3\le 11 \\ \Rightarrow 2x\le 11+3 \\ \Rightarrow 2x\le 14 \\ \Rightarrow x\le \frac{14}{2} \\ \Rightarrow x\le 7 \end{gathered}$$

Therefore $x\in (-6,7]$

Hence, option (A) is the correct .