IMO Algebra and Equations 2 — Questions and Answers
Question 1: Solve: 4x − 6 = 2x + 8
- 5
- 7 (Correct answer)
- 9
- 11
Correct answer: 7
4x − 2x = 8 + 6 → 2x = 14 → x = 7.
Question 2: What is the value of x² + 2x when x = 3?
- 9
- 12
- 15 (Correct answer)
- 18
Correct answer: 15
x² + 2x = 3² + 2(3) = 9 + 6 = 15.
Question 3: Which of the following is a linear equation?
- y = x²
- y = x³ + 1
- y = 3x + 2 (Correct answer)
- y = 1/x
Correct answer: y = 3x + 2
y = 3x + 2 is a linear equation because the highest power of x is 1.
Question 4: If 5n = 45, what is n?
- 7
- 8
- 9 (Correct answer)
- 10
Correct answer: 9
n = 45 ÷ 5 = 9.
Question 5: Simplify: 3(2x − 4) + 5
- 6x − 7 (Correct answer)
- 6x − 1
- 6x + 5
- 5x − 7
Correct answer: 6x − 7
3(2x − 4) + 5 = 6x − 12 + 5 = 6x − 7.
Question 6: The sum of two numbers is 50. One number is 18. What is the other?
- 28
- 30
- 32 (Correct answer)
- 34
Correct answer: 32
Other number = 50 − 18 = 32.
IMO Algebra and Equations 2
Solve: 4x − 6 = 2x + 8