WAEC 2010 Mathematics · Question 42
The mean of the numbers 2, 5, 2x and 7 is less than or equal to 5. Find the range of the values of x
Options
- A.x 3
- B.x 3
- C.x < 3
- D.x > 3
Answer: A. x 3
Explanation written with AI and checked against the answer key
Analyze the question: We have four numbers: 2, 5, 2x and 7. Their mean must be less than or equal to 5, and we need the values of x that satisfy this. Concept: Mean = (sum of the numbers) ÷ (how many numbers there are). Solution: Sum = 2 + 5 + 2x + 7 = 14 + 2x Mean = (14 + 2x) / 4 The condition is: (14 + 2x) / 4 ≤ 5 Multiply both sides by 4 (a positive number, so the inequality sign stays the same): 14 + 2x ≤ 20 Subtract 14 from both sides: 2x ≤ 6 Divide by 2: x ≤ 3 Check: If x = 3, the numbers are 2, 5, 6, 7. The sum is 20 and the mean is 5, which satisfies "less than or equal to 5". If x = 2, the numbers are 2, 5, 4, 7. The sum is 18 and the mean is 4.5, which is less than 5. So the answer works. Answer: A (x ≤ 3) Tip: Pay attention to the wording "less than or equal to". The "equal to" part means you must use ≤, not <, so option C is wrong. Also, only flip the inequality sign when you multiply or divide by a negative number. Here we divided by positive numbers, so the sign stayed the same.AI can make mistakes. Report anything that looks wrong.
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