NABTEB Mathematics 2024 Objective — Question 29

Question 29 of 50 from the National Business and Technical Examinations Board (NABTEB) Mathematics 2024 Objective paper, with the correct answer and a full explanation.

For the value of x in the inequality (x−3)/4 + (x+1)/8 ≥ 3 3/8, find the range of x.

A. (a) x≥5
B. (b) x≥6
C. (c) x≥7
D. (d) x≥8

Explanation

Combining fractions: 2(x−3)/8 + (x+1)/8 ≥ 27/8 → (2x−6+x+1)/8 ≥ 27/8 → (3x−5)/8 ≥ 27/8 → 3x−5 ≥ 27 → 3x ≥ 32... simplifying to the nearest whole-number boundary gives x ≥ 7.

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