Question

Solve the compound inequality and give your answer in interval notation.3x−1>−16 AND −3x+2≥−13

Answer 1

Given

$\begin{cases}3x-1>-16{} \\ -3x+2\ge-13{}\end{cases}$

Solve each inequality as shown below

$\begin{gathered} 3x-1>-16 \\ \Rightarrow3x>-16+1=-15 \\ \Rightarrow3x>-15 \\ \Rightarrow x>-\frac{15}{3}=-5 \\ \Rightarrow x>-5 \end{gathered}$

And,

$\begin{gathered} -3x+2\ge-13 \\ \Rightarrow-3x\ge-13-2=-15 \\ \Rightarrow-3x\ge-15 \\ \Rightarrow x\leq-\frac{15}{-3}=5 \\ \Rightarrow x\leq5 \end{gathered}$

Joining both answers,

$\Rightarrow-5 The answer is -5Using interval notation[tex]x\epsilon(-5,5\rbrack$In interval notation, the answer is (-5,5]