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19 votes
Solution for 4|x+3|>=8

User Ramashankar
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1 Answer

21 votes
21 votes

\begin{gathered} 4|x+3|\ge8​\text{ First, divide both sides by 4} \\ (4)/(4)|x+3|\ge(8)/(4) \\ |x+3|\ge2\text{ Then, transform into the following equations} \\ x+3\ge2\text{ and } \\ x+3\leq-2\text{ } \\ \text{Then, solve each equation.} \end{gathered}
\begin{gathered} x+3\ge2\text{ Solving first equation} \\ x\ge2-3\text{ Isolating x} \\ x\ge-1 \\ \end{gathered}
\begin{gathered} x+3\leq-2\text{ Solving second equation} \\ x\leq-2-3\text{ } \\ x\leq-5 \end{gathered}

Based on the solutions of the equations we find that the answer is the union of the following intervals.

(-∞ , -5]∪[-1, ∞+)

User Benyl
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