SATs Algebraic Expressions & Equations 3 — Questions and Answers
Question 1: The sum of three consecutive integers is 57. What is the largest of the three integers?
- 17
- 18
- 19 (Correct answer)
- 20
Correct answer: 19
Let the integers be n, n+1, n+2; then 3n + 3 = 57, so n = 18 and the largest is 20.
Question 2: Which of the following is equivalent to (3x² − 2x + 5) − (x² + 4x − 3)?
- 2x² − 6x + 8 (Correct answer)
- 2x² + 2x + 2
- 4x² + 2x + 2
- 2x² − 6x + 2
Correct answer: 2x² − 6x + 8
Distributing the minus sign: (3x²−x²) + (−2x−4x) + (5+3) = 2x² − 6x + 8.
Question 3: If 5 − 2x > 11, which of the following must be true?
- x > 3
- x < −3 (Correct answer)
- x > −3
- x < 3
Correct answer: x < −3
Subtracting 5: −2x > 6; dividing by −2 and flipping: x < −3.
Question 4: What is the product of (2x + 3) and (x − 4)?
- 2x² − 5x − 12 (Correct answer)
- 2x² + 5x − 12
- 2x² − 8x − 12
- 2x² − 5x + 12
Correct answer: 2x² − 5x − 12
FOIL: 2x·x + 2x·(−4) + 3·x + 3·(−4) = 2x² − 8x + 3x − 12 = 2x² − 5x − 12.
Question 5: If y = 3x − 7 and y = 5, what is x?
- 4 (Correct answer)
- −4
- 4/3
- 6
Correct answer: 4
Substituting: 3x − 7 = 5, so 3x = 12, giving x = 4.
Question 6: A rectangular garden has a perimeter of 54 feet. If the length is 3 feet more than twice the width, what is the width?
- 8 feet
- 9 feet (Correct answer)
- 12 feet
- 7.5 feet
Correct answer: 9 feet
With l = 2w + 3, the perimeter equation 2(w + 2w + 3) = 54 gives w = 9.
Question 7: What is the solution to the equation x/3 + 5 = x/2 − 1?
- x = 36 (Correct answer)
- x = −36
- x = 12
- x = −12
Correct answer: x = 36
Multiplying through by 6: 2x + 30 = 3x − 6, so x = 36.
SATs Algebraic Expressions & Equations 3
The sum of three consecutive integers is 57.
What is the largest of the three integers?