Keystone Test Algebra: Linear Equations/Inequalities 2 — Questions and Answers
Question 1: A gym charges a $30 registration fee plus $25 per month. If a member spent a total of $205, how many months did they pay for?
- 6
- 7 (Correct answer)
- 8
- 5
Correct answer: 7
Set up 30 + 25m = 205; subtract 30 to get 25m = 175, so m = 7.
Question 2: Which value of x satisfies 4(x − 3) = 2x + 6?
- 6
- 9 (Correct answer)
- 3
- 12
Correct answer: 9
Distribute to get 4x − 12 = 2x + 6; subtract 2x and add 12 to get 2x = 18, so x = 9.
Question 3: What is the solution to the inequality 3x + 7 ≥ 22?
- x ≤ 5
- x ≥ 5 (Correct answer)
- x ≤ 29
- x ≥ 29
Correct answer: x ≥ 5
Subtract 7 from both sides: 3x ≥ 15, then divide by 3: x ≥ 5.
Question 4: A line passes through (0, −4) and has a slope of 3. What is the equation of the line?
- y = 3x + 4
- y = −4x + 3
- y = 3x − 4 (Correct answer)
- y = −3x + 4
Correct answer: y = 3x − 4
Using slope-intercept form y = mx + b with m = 3 and b = −4 gives y = 3x − 4.
Question 5: If 2(y + 5) − 3y = 1, what is the value of y?
- 9 (Correct answer)
- −9
- 11
- −11
Correct answer: 9
Distribute: 2y + 10 − 3y = 1; combine: −y + 10 = 1; so −y = −9, giving y = 9.
Question 6: Which graph represents the solution to x − 4 < 2?
- An open circle at 6 with shading to the right
- A closed circle at 6 with shading to the right
- An open circle at 6 with shading to the left (Correct answer)
- A closed circle at 6 with shading to the left
Correct answer: An open circle at 6 with shading to the left
Solving gives x < 6, which is graphed as an open circle at 6 with shading to the left.
Question 7: A company rents cars for $45 per day plus $0.20 per mile. If a customer paid $89, how many miles did they drive?
- 175
- 200
- 220 (Correct answer)
- 245
Correct answer: 220
Set up 45 + 0.20m = 89; subtract 45 to get 0.20m = 44, so m = 220.
Keystone Test Algebra: Linear Equations/Inequalities 2
A gym charges a $30 registration fee plus $25 per month.
If a member spent a total of $205, how many months did they pay for?