ALEKS Linear Equations and Inequalities 2 — Questions and Answers
Question 1: Solve for y: 2y + 6 = 18
- y = 6 (Correct answer)
- y = 12
- y = 3
- y = 9
Correct answer: y = 6
Subtracting 6 from both sides gives 2y = 12, and dividing by 2 gives y = 6.
Question 2: What is the y-intercept of the line y = −2x + 4?
- −2
- 2
- 4 (Correct answer)
- −4
Correct answer: 4
In slope-intercept form y = mx + b, the y-intercept is the constant b = 4.
Question 3: Solve: 3(x − 2) = 12
- x = 2
- x = 6 (Correct answer)
- x = 4
- x = 14/3
Correct answer: x = 6
Distributing gives 3x − 6 = 12, then adding 6 yields 3x = 18, so x = 6.
Question 4: Which value is a solution to 2x − 3 > 7?
- x = 4
- x = 5
- x = 6 (Correct answer)
- x = 3
Correct answer: x = 6
Adding 3 gives 2x > 10, so x > 5; only x = 6 satisfies this condition.
Question 5: What is the x-intercept of y = 2x − 8?
- (0, −8)
- (4, 0) (Correct answer)
- (−4, 0)
- (8, 0)
Correct answer: (4, 0)
Setting y = 0 gives 2x = 8, so x = 4, making the x-intercept the point (4, 0).
Question 6: Solve: −3x + 9 = 0
- x = −3
- x = 3 (Correct answer)
- x = 27
- x = −9
Correct answer: x = 3
Subtracting 9 gives −3x = −9, and dividing both sides by −3 gives x = 3.
Question 7: Which compound inequality represents 'n is greater than −2 and less than 6'?
- −2 ≤ n ≤ 6
- −2 < n < 6 (Correct answer)
- n > 6
- n < −2
Correct answer: −2 < n < 6
'Greater than −2 and less than 6' uses strict inequalities (not including endpoints), written as −2 < n < 6.
