WAEC 2024 Mathematics · Question 18

For what values of x is $\frac{x - 3}{4}$ + $\frac{x + 1}{8}$ $\geq$ 2 ?

Options

A.x $\geq$ 5
B.x $\geq$ 6
C.x $\geq$ 7
D.x $\geq$ 8

Answer: C. x $\geq$ 7

Explanation written with AI and checked against the answer key

Step 1: Analyze the question We need all values of x that satisfy the inequality (x − 3)/4 + (x + 1)/8 ≥ 2. Step 2: Concept To solve an inequality with fractions, multiply every term by the LCM of the denominators. Because the LCM is positive, the inequality sign does not change. Step 3: Solution The LCM of 4 and 8 is 8. Multiply every term by 8: 8·(x − 3)/4 + 8·(x + 1)/8 ≥ 8·2 2(x − 3) + (x + 1) ≥ 16 2x − 6 + x + 1 ≥ 16 3x − 5 ≥ 16 3x ≥ 21 x ≥ 7 Check: Let x = 7: (7 − 3)/4 + (7 + 1)/8 = 1 + 1 = 2, which equals 2, so the boundary is correct. Try x = 8: 5/4 + 9/8 = 19/8 = 2.375 ≥ 2 ✓. Step 4: Answer x ≥ 7, which is option C. Tip: In inequality questions, always clear the fractions first using the LCM. Then plug the boundary value back in to confirm that it gives equality. Only flip the inequality sign if you multiply or divide by a negative number.

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For what values of x is x−34\frac{x - 3}{4}4x−3​ + x+18\frac{x + 1}{8}8x+1​ ≥\geq≥ 2 ?

Options

Answer: C. x ≥\geq≥ 7

For what values of x is $\frac{x - 3}{4}$ + $\frac{x + 1}{8}$ $\geq$ 2 ?

Answer: C. x $\geq$ 7