Question:
\( -5<x \le -1 \) implies \( -21<5x + 4 \le b \), the least value of \( b \) is
\( -5<x \le -1 \) implies \( -21<5x + 4 \le b \), the least value of \( b \) is
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Transform inequalities step-by-step and track interval endpoints carefully.
Updated On: Apr 21, 2026
- \(5 \)
- \(-5 \)
- \(-4 \)
- \(4 \)
- \(-1 \)
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The Correct Option is
Solution and Explanation
Concept:
Find the range of \( 5x+4 \) using given bounds of \(x\).
Step 1: Use interval transformation.
\[ -5<x \le -1 \] Multiply by 5: \[ -25<5x \le -5 \] Add 4: \[ -21<5x + 4 \le -1 \]
Step 2: Compare with given form.
\[ -21<5x + 4 \le b \] Thus, \[ b = -1 \]
Step 1: Use interval transformation.
\[ -5<x \le -1 \] Multiply by 5: \[ -25<5x \le -5 \] Add 4: \[ -21<5x + 4 \le -1 \]
Step 2: Compare with given form.
\[ -21<5x + 4 \le b \] Thus, \[ b = -1 \]
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