Multiple Choice
Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(B)
7
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9. Inequalities and Absolute Value
Absolute Value Inequalities
Multiple Choice
Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(A)
A
B
C
D
Verified step by step guidance1
Start with the given inequality: \(\left|\frac{2x - 5}{3}\right| \le \frac{1}{3}\). The absolute value inequality \(|A| \le B\) means that \(-B \le A \le B\).
Apply this property to the inequality: \(-\frac{1}{3} \le \frac{2x - 5}{3} \le \frac{1}{3}\).
Multiply all parts of the inequality by 3 to eliminate the denominator: \(-1 \le 2x - 5 \le 1\).
Next, add 5 to all parts of the inequality to isolate the term with \(x\): \(-1 + 5 \le 2x \le 1 + 5\), which simplifies to \(4 \le 2x \le 6\).
Finally, divide all parts by 2 to solve for \(x\): \(\frac{4}{2} \le x \le \frac{6}{2}\), which simplifies to \(2 \le x \le 3\). Express this solution in interval notation as \([2, 3]\).
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