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Solve the following inequality algebraically. 5 |x + 4| – 4 => 36

User Hackattack
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1 Answer

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To solve the inequality we have to remember the property:


\lvert x\rvert\ge a\Leftrightarrow x\ge a\lor x\leq-a

Then:


\begin{gathered} 5\lvert x+4\rvert-4\ge36 \\ 5\lvert x+4\rvert\ge40 \\ \lvert x+4\rvert\ge(40)/(5) \\ x+4\ge8\lor x+4\leq-8 \\ x\ge8-4\lor x\leq-8-4 \\ x\ge4\lor x\leq-12 \end{gathered}

Therefore the solution is:


(-\infty,-12\rbrack\cup\lbrack4,\infty)

User Pradeep Goswami
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