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

Solve the compound inequality and give your answer in interval notation.3x−1>−16 AND-example-1
User Nakul Narayanan
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1 Answer

13 votes
13 votes

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\rbrackIn interval notation, the answer is (-5,5]
User Pedro Ghilardi
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