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WAEC 2022 Mathematics · Question 37

.Find the value of x such that 1x\frac{1}{x} +43x\frac{4}{3x} - 56x\frac{5}{6x} + 1 = 0

Options

  1. A.16\frac{1}{6}
  2. B.14\frac{1}{4}
  3. C.−32\frac{-3}{2}
  4. D.−76\frac{-7}{6}

Answer: C. −32\frac{-3}{2}

Explanation written with AI and checked against the answer key

Analyze the question: We need the value of x that satisfies 1/x + 4/(3x) − 5/(6x) + 1 = 0. Concept: Terms with the same denominator x can be combined by finding a common denominator for the fractions. Then we solve the resulting simple equation. Solution: Combine the three fractions using the common denominator 6x: 1/x = 6/(6x) 4/(3x) = 8/(6x) 5/(6x) = 5/(6x) So: 6/(6x) + 8/(6x) − 5/(6x) = 9/(6x) = 3/(2x) The equation becomes: 3/(2x) + 1 = 0 3/(2x) = −1 3 = −2x x = −3/2 Check: 1/x = −2/3, 4/(3x) = 4/(−9/2) = −8/9, 5/(6x) = 5/(−9) = −5/9. −2/3 − 8/9 + 5/9 + 1 = −6/9 − 8/9 + 5/9 + 9/9 = 0 ✓ Answer: x = −3/2, which is option C. Tip: When every fraction has x in the denominator, add the numerators over one common denominator first. Then you only have one fraction to deal with. Always substitute your answer back to check it.

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