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>-(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-(15)/(-3)=5 \\ \Rightarrow x\leq5 \end{gathered}`

Joining both answers,

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