Solve the equation x – (1 + ³ˣ⁄₂)/4 = (2 – ˣ⁄₄)/3 – 28/12

JAMB Mathematics 2023 56 views

Solve the equation x – (1 + ³ˣ⁄₂)/4 = (2 – ˣ⁄₄)/3 – 28/12

  1. 4
  2. -3
  3. 1
  4. -2 ✓

Explanation

Step 1: Find LCD (Least Common Denominator)
LCD of 2, 3, 4, and 12 is 12

Step 2: Multiply entire equation by 12
12x – 12(1 + 3x/2)/4 = 12(2 – x/4)/3 – 12(28/12)

Step 3: Simplify each term
Left: 12x – 3(1 + 3x/2) = 12x – 3 – 9x/2
Right: 4(2 – x/4) – 28 = 8 – x – 28

Step 4: Clear remaining fractions
Multiply by 2: 24x – 6 – 9x = 16 – 2x – 56
15x – 6 = -2x – 40

Step 5: Solve for x
15x + 2x = -40 + 6
17x = -34
x = -2

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