Solve the inequality (x - 3)(x - 4) \(\leq\) 0

Mathematics

JAMB 1995

A. 3 \(\leq\) x \(\leq\) 4
B. 3 < x < 4
C. 3 \(\leq\) x < 4
D. 3 < x \(\leq\) 4

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Correct Answer: Option A

Explanation

(x - 3)(x - 4) \(\leq\) 0

Case 1 (+, -) = x - 3 \(\geq\) 0, X - 4 \(\geq\) 0

= X \(\leq\) 3, x \(\geq\) 4

= 3 < x \(\geq\) 4 (solution)

Case 2 = (-, +) = x - 3 \(\leq\) 0, x - 4 \(\geq\) 0

= x \(\leq\) 3, x \(\geq\) 4

therefore = 3 \(\leq\) x \(\leq\) 4

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