Keystone Test Algebra: Linear Equations/Inequalities 3 — Questions and Answers
Question 1: Which of the following is equivalent to 5 − 2(x + 3) = 7?
- 5 − 2x − 6 = 7 (Correct answer)
- 5 − 2x + 3 = 7
- 5 + 2x + 6 = 7
- 5 − 2x + 6 = 7
Correct answer: 5 − 2x − 6 = 7
Distributing −2 over (x + 3) gives −2x − 6, so the equation becomes 5 − 2x − 6 = 7.
Question 2: What is the x-intercept of the line y = 2x − 10?
- (0, −10)
- (5, 0) (Correct answer)
- (10, 0)
- (−5, 0)
Correct answer: (5, 0)
Set y = 0 and solve: 0 = 2x − 10 gives 2x = 10, so x = 5; the x-intercept is (5, 0).
Question 3: Solve: (x/3) + 4 = 7
- x = 1
- x = 3
- x = 9 (Correct answer)
- x = 33
Correct answer: x = 9
Subtract 4 from both sides: x/3 = 3; multiply both sides by 3: x = 9.
Question 4: A number is doubled and then decreased by 11. The result is 13. What is the number?
- 10
- 12 (Correct answer)
- 1
- 2
Correct answer: 12
Translate to 2n − 11 = 13; add 11: 2n = 24; divide by 2: n = 12.
Question 5: Which inequality has x = −2 as a solution?
- x + 5 > 4
- 2x − 1 ≥ −5 (Correct answer)
- x − 1 < −4
- 3x > −3
Correct answer: 2x − 1 ≥ −5
Substituting x = −2 into 2x − 1 ≥ −5 gives 2(−2) − 1 = −5 ≥ −5, which is true.
Question 6: Two friends share a bag of apples. One friend takes 3 more than twice what the other takes. Together they have 24 apples. How many does the first friend take?
- 7
- 17 (Correct answer)
- 9
- 15
Correct answer: 17
Let x = second friend's apples; first takes 2x + 3; equation: x + 2x + 3 = 24 → 3x = 21 → x = 7, so first takes 17.
Question 7: Which of the following represents a linear equation?
- y = x² + 2
- y = 3/x
- y = 2x − 5 (Correct answer)
- y = x³
Correct answer: y = 2x − 5
y = 2x − 5 is linear because the variable x has an exponent of 1 and forms a straight line.
Keystone Test Algebra: Linear Equations/Inequalities 3
Which of the following is equivalent to 5 − 2(x + 3) = 7?