Multiple Choice
Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(A)
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2. Linear Equations and Inequalities
Absolute Value Inequalities
Multiple Choice
Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(B)
A
B
C
OR
D
OR
Verified step by step guidance1
Start with the given inequality: \(\frac{1}{2} \left| 2x + 4 \right| + 5 \geq 8\).
Isolate the absolute value expression by subtracting 5 from both sides: \(\frac{1}{2} \left| 2x + 4 \right| \geq 8 - 5\).
Simplify the right side: \(\frac{1}{2} \left| 2x + 4 \right| \geq 3\).
Multiply both sides of the inequality by 2 to eliminate the fraction: \(\left| 2x + 4 \right| \geq 6\).
Recall that for an absolute value inequality \(|A| \geq B\) (where \(B > 0\)), the solution splits into two cases: \(A \leq -B\) or \(A \geq B\). Apply this to get two inequalities: \(2x + 4 \leq -6\) or \(2x + 4 \geq 6\).
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