SATs Algebraic Expressions & Equations 2 — Questions and Answers
Question 1: If 3(x − 4) = 2x + 1, what is the value of x?
- 11
- 13 (Correct answer)
- 7
- 5
Correct answer: 13
Distributing gives 3x − 12 = 2x + 1, so x = 13.
Question 2: Which expression is equivalent to 4x² − 9?
- (2x − 3)(2x − 3)
- (4x − 3)(x + 3)
- (2x + 3)(2x − 3) (Correct answer)
- (2x − 9)(2x + 1)
Correct answer: (2x + 3)(2x − 3)
4x² − 9 is a difference of squares: (2x)² − 3² = (2x + 3)(2x − 3).
Question 3: A store sells pens for $1.50 each and notebooks for $3.00 each. Maria spent $18 buying a total of 8 items. How many pens did she buy?
- 2
- 4 (Correct answer)
- 6
- 3
Correct answer: 4
Setting up p + n = 8 and 1.5p + 3n = 18, solving gives p = 4.
Question 4: What is the value of the expression 2a² − 3b when a = −3 and b = 4?
- 6 (Correct answer)
- 30
- −12
- 18
Correct answer: 6
2(−3)² − 3(4) = 2(9) − 12 = 18 − 12 = 6.
Question 5: If (x + 5)(x − 2) = 0, what are the solutions for x?
- x = 5 and x = −2
- x = −5 and x = 2 (Correct answer)
- x = −5 and x = −2
- x = 5 and x = 2
Correct answer: x = −5 and x = 2
Setting each factor to zero: x + 5 = 0 gives x = −5, and x − 2 = 0 gives x = 2.
Question 6: Which value(s) of x satisfy |2x − 6| = 10?
- x = 8 only
- x = −2 only
- x = 8 or x = −2 (Correct answer)
- x = 2 or x = 8
Correct answer: x = 8 or x = −2
2x − 6 = 10 gives x = 8, and 2x − 6 = −10 gives x = −2.
Question 7: Which of the following is a correct simplification of 5x² − 3x + 2x² + 7x?
- 7x² + 4x (Correct answer)
- 3x² + 10x
- 7x² − 4x
- 10x² + 4x
Correct answer: 7x² + 4x
Combine like terms: (5x² + 2x²) + (−3x + 7x) = 7x² + 4x.
SATs Algebraic Expressions & Equations 2
If 3(x − 4) = 2x + 1, what is the value of x?