DeeepSolve Logo
DeeepSolve
Get app

WAEC 2013 Mathematics · Question 28

Solve the inequality: 2x−52<(2−x)\frac{2x - 5}{2} < (2 - x)

Options

  1. A.x > 0
  2. B.x < 14\frac{1}{4}
  3. C.x > 212\frac{1}{2}
  4. D.x < 214\frac{1}{4}

Answer: D. x < 214\frac{1}{4}

Explanation written with AI and checked against the answer key

Analyze the question: We need to find the values of x that satisfy (2x − 5)/2 < 2 − x. Concept: To solve a linear inequality, clear the fraction by multiplying both sides by a positive number (the inequality sign stays the same). Then collect the x-terms on one side and the numbers on the other. Only flip the sign if you multiply or divide by a negative number. Solution: Step 1: Multiply both sides by 2 (positive, so the sign stays): 2x − 5 < 2(2 − x) 2x − 5 < 4 − 2x Step 2: Collect x-terms on the left by adding 2x to both sides: 4x − 5 < 4 Step 3: Add 5 to both sides: 4x < 9 Step 4: Divide by 4: x < 9/4 = 2¼ Check: Try x = 2 (which is less than 2¼): LHS = (4 − 5)/2 = −0.5, RHS = 2 − 2 = 0. Since −0.5 < 0, it works. Try x = 3: LHS = 0.5, RHS = −1. Since 0.5 < −1 is false, it fails. This confirms that x < 2¼. Answer: Option D, x < 2¼. Tip: Always test a number in your final answer, one inside the range and one outside. It takes only seconds and catches sign errors. Also, remember that the inequality sign flips only when you multiply or divide by a negative number.

AI can make mistakes. Report anything that looks wrong.

Practise similar questionsGet step-by-step help on DeeepSolve

Past questions © the examination body (JAMB/WAEC/NECO). DeeepSolve is not affiliated with them. Rights holders: see /copyright.