Solve the inequality. Express you answer in interval notation. -3(x + 2) > 15 or x-3< -1

Wiktoria Prusik asked Dec 19, 2023

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Wiktoria Prusik asked Dec 19, 2023

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SOLUTION

We are told to solve the inequality

$-3\mleft(x+2\mright)>15\text{ or }x-3<-1$

This becomes

$\begin{gathered} -3(x+2)>15\text{ or }x-3<-1 \\ -3x-6>15\text{ or }x<2 \\ -3x>11\text{ or }x<2 \\ x<-(11)/(3)\text{ or }x<2 \end{gathered}$

In interval notation, this becomes

$(-\infty,-(11)/(3))\cup(-\infty,2)$

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