Mcdonald Craig
09/26/2023 · Elementary School

Solve the absolute value inequality. \[ 2|2 x-3|+2>12 \] Select the correct choice below and, if necessary, fill in the answer box to con A. The solution set in interval notation is (Simplify your answer.) B. The solution set is \( \varnothing \).

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Solve the equation \( 2|2x-3|+2>12 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(2\left|2x-3\right|+2>12\) - step1: Move the expression to the left side: \(2\left|2x-3\right|+2-12>0\) - step2: Subtract the numbers: \(2\left|2x-3\right|-10>0\) - step3: Rewrite the expression: \(2\left|2x-3\right|>10\) - step4: Divide both sides: \(\frac{2\left|2x-3\right|}{2}>\frac{10}{2}\) - step5: Divide the numbers: \(\left|2x-3\right|>5\) - step6: Separate into possible cases: \(\begin{align}&2x-3>5\\&2x-3<-5\end{align}\) - step7: Solve the inequality: \(\begin{align}&x>4\\&x<-1\end{align}\) - step8: Find the union: \(x \in \left(-\infty,-1\right)\cup \left(4,+\infty\right)\) The solution to the absolute value inequality \(2|2x-3|+2>12\) is \(x \in (-\infty,-1) \cup (4,+\infty)\). Therefore, the correct choice is: A. The solution set in interval notation is \((- \infty, -1) \cup (4, +\infty)\).

Quick Answer

A. The solution set in interval notation is \((- \infty, -1) \cup (4, +\infty)\).
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