JAMB 2019 Mathematics · Question 70
Find the value of x for
Options
- A.x -5
- B.x -1
- C.x -1
- D.x 3
Answer: C. x -1
Explanation written with AI and checked against the answer key
Analyze the question: We need to solve a linear inequality with fractions. The method is to clear the denominators by multiplying by the LCM, then collect like terms. Concept: Multiply both sides by a positive number and the inequality sign stays the same. Divide or multiply by a negative number and the sign flips. Solution: Given: (2 + 2x)/3 − 2 ≥ (4x − 6)/5 Step 1: The LCM of 3 and 5 is 15. Multiply every term by 15: 5(2 + 2x) − 30 ≥ 3(4x − 6) Step 2: Expand: 10 + 10x − 30 ≥ 12x − 18 Step 3: Simplify the left side: 10x − 20 ≥ 12x − 18 Step 4: Collect like terms. Subtract 12x from both sides and add 20 to both sides: 10x − 12x ≥ −18 + 20 −2x ≥ 2 Step 5: Divide by −2, which flips the sign: x ≤ −1 Check: Take x = −2. Left side: (2 − 4)/3 − 2 = −2/3 − 2 = −8/3 ≈ −2.67. Right side: (−8 − 6)/5 = −14/5 = −2.8. Since −2.67 ≥ −2.8, it works. Take x = 0: left = 2/3 − 2 = −4/3 ≈ −1.33, right = −6/5 = −1.2. Since −1.33 ≥ −1.2 is false, x = 0 fails, which is consistent with x ≤ −1. Answer: x ≤ −1, which is option C. Tip: Whenever you divide or multiply an inequality by a negative number, flip the sign. Many students lose marks here. Also, a quick test with a number from your answer range, as done above, takes only seconds and confirms your result.AI can make mistakes. Report anything that looks wrong.
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