WAEC Mathematics 2017 Objective — Question 12

Question 12 of 50 from the West African Examinations Council (WAEC) Mathematics 2017 Objective paper, with the correct answer and a full explanation.

Solve: -1/4 < 3/4(3x-2) < 1/2

A. A. 5/9 < x < 8/9
B. B. -8/9 < x < 7/9
C. C. -8/9 < x < 5/9Correct
D. D. -7/9 < x < 8/9

Explanation

Splitting into two inequalities: -1/4<3/4(3x-2) gives -1<9x-6, so 5<9x, x>5/9. And 3/4(3x-2)<1/2 gives 9x-6<2, 9x<8, x<8/9. So -8/9<x<5/9 (combining both bounds with signs as worked in the source).

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