Question:
The set of all \(x\) satisfying the inequality \(|3 - 4x| \leq 11\) is
The set of all \(x\) satisfying the inequality \(|3 - 4x| \leq 11\) is
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When dividing an inequality by a negative number, reverse the inequality signs.
Updated On: Apr 25, 2026
- \([-2, 7]\)
- \([-2, \frac{7}{2}]\)
- \([-7, 2]\)
- \([-\frac{7}{2}, 2]\)
- \([-2, -2]\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
\(|3 - 4x| \leq 11\) means \(-11 \leq 3 - 4x \leq 11\).
Step 2: Detailed Explanation:
\(-11 \leq 3 - 4x \leq 11\)
Subtract 3: \(-14 \leq -4x \leq 8\)
Divide by -4 (reverse inequality signs): \(-2 \leq x \leq \frac{7}{2}\)
Thus \(x \in \left[-2, \frac{7}{2}\right]\).
Step 3: Final Answer:
\(\left[-2, \frac{7}{2}\right]\).
\(|3 - 4x| \leq 11\) means \(-11 \leq 3 - 4x \leq 11\).
Step 2: Detailed Explanation:
\(-11 \leq 3 - 4x \leq 11\)
Subtract 3: \(-14 \leq -4x \leq 8\)
Divide by -4 (reverse inequality signs): \(-2 \leq x \leq \frac{7}{2}\)
Thus \(x \in \left[-2, \frac{7}{2}\right]\).
Step 3: Final Answer:
\(\left[-2, \frac{7}{2}\right]\).
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