BMST Algebraic Equations and Inequalities 5 — Questions and Answers
Question 1: Solve for y: 7y + 3 = 5y + 11
- y = 4 (Correct answer)
- y = -4
- y = 7
- y = 2
Correct answer: y = 4
Subtract 5y from both sides to get 2y + 3 = 11, then subtract 3 and divide by 2 to get y = 4.
Question 2: If 3x + 2 = 17, what is the value of 6x?
- 5
- 10
- 30 (Correct answer)
- 34
Correct answer: 30
Solving gives 3x = 15, so x = 5, and 6x = 30.
Question 3: A rectangle has length (2x + 3) and width 4. If the perimeter is 38, find x.
- x = 3
- x = 4
- x = 6 (Correct answer)
- x = 7
Correct answer: x = 6
Using P = 2l + 2w: 2(2x+3) + 2(4) = 38 gives 4x + 14 = 38, so 4x = 24 and x = 6.
Question 4: Solve the inequality: 2x - 3 < 7. What is the boundary value?
- x = 2
- x = 5 (Correct answer)
- x = 7
- x = 10
Correct answer: x = 5
Adding 3 to both sides gives 2x < 10, then dividing by 2 gives x < 5, so the boundary is 5.
Question 5: Which equation is equivalent to 4(x - 2) = 12?
- 4x = 10
- 4x - 2 = 12
- 4x = 20 (Correct answer)
- x - 2 = 3
Correct answer: 4x = 20
Distributing gives 4x - 8 = 12, and adding 8 to both sides gives 4x = 20.
Question 6: At a car wash, each car costs $8. Revenue must exceed $120 to cover costs. What is the minimum number of cars needed?
- 14
- 15
- 16 (Correct answer)
- 17
Correct answer: 16
The inequality 8c > 120 gives c > 15, so at least 16 cars (the next whole number) are needed.
Question 7: Which of the following is NOT a solution to the inequality x ≥ -5?
- x = -5
- x = 0
- x = -6 (Correct answer)
- x = 100
Correct answer: x = -6
x = -6 is less than -5 and does not satisfy x ≥ -5; all other values are greater than or equal to -5.
BMST Algebraic Equations and Inequalities 5
Solve for y: 7y + 3 = 5y + 11