BMST Algebraic Equations and Inequalities 4 — Questions and Answers
Question 1: Solve for x: x² = 49
- x = 7 only
- x = -7 only
- x = 7 or x = -7 (Correct answer)
- x = 24.5
Correct answer: x = 7 or x = -7
Taking the square root of both sides gives x = ±7, since both 7² and (-7)² equal 49.
Question 2: A store sells pens for $2 each. Maria spends no more than $14. What is the maximum number of pens she can buy?
- 6
- 7 (Correct answer)
- 8
- 28
Correct answer: 7
The inequality 2p ≤ 14 gives p ≤ 7, so she can buy at most 7 pens.
Question 3: Solve for b: b/4 - 2 = 3
- b = 4
- b = 20 (Correct answer)
- b = 5
- b = 1
Correct answer: b = 20
Add 2 to both sides to get b/4 = 5, then multiply by 4 to get b = 20.
Question 4: Which equation has no solution?
- x + 3 = 3 + x
- 2x = 2x + 1 (Correct answer)
- x = x
- 3 = 3
Correct answer: 2x = 2x + 1
2x = 2x + 1 simplifies to 0 = 1, which is a contradiction with no solution.
Question 5: Solve: -2(x - 4) = 10
- x = -1 (Correct answer)
- x = 1
- x = 9
- x = -9
Correct answer: x = -1
Distribute to get -2x + 8 = 10, subtract 8 to get -2x = 2, then divide by -2 to get x = -1.
Question 6: The sum of three consecutive integers is 48. What is the smallest integer?
- 14
- 15 (Correct answer)
- 16
- 17
Correct answer: 15
Let the integers be n, n+1, n+2; then 3n + 3 = 48 gives 3n = 45, so n = 15.
Question 7: Which value satisfies both x > -3 and x ≤ 1?
- x = -4
- x = 2
- x = -3
- x = 0 (Correct answer)
Correct answer: x = 0
x = 0 satisfies 0 > -3 (true) and 0 ≤ 1 (true); the other values fail at least one condition.
