Math Linear Equations, Inequalities, and Systems — Questions and Answers
Question 1: Solve for x: 3(x − 2) + 4 = 2x + 7
- x = 9 (Correct answer)
- x = 3
- x = 5
- x = 7
Correct answer: x = 9
3x − 6 + 4 = 2x + 7 → 3x − 2 = 2x + 7 → x = 9.
Question 2: Which value of x satisfies the inequality 2x − 5 > 3?
- x = 5 (Correct answer)
- x = 3
- x = 4
- x = 2
Correct answer: x = 5
2x − 5 > 3 → 2x > 8 → x > 4. Only x = 5 is greater than 4.
Question 3: Solve the system: x + y = 10 and 2x − y = 5
- x = 5, y = 5 (Correct answer)
- x = 3, y = 7
- x = 7, y = 3
- x = 6, y = 4
Correct answer: x = 5, y = 5
Add the equations: 3x = 15 → x = 5. Substitute: 5 + y = 10 → y = 5.
Question 4: What is the slope of the line passing through (2, 3) and (6, 11)?
- 2 (Correct answer)
- 1/2
- 4
- 8
Correct answer: 2
Slope = (y₂ − y₁)/(x₂ − x₁) = (11 − 3)/(6 − 2) = 8/4 = 2.
Question 5: A line has equation y = −3x + 7. What is the y-intercept?
- 7 (Correct answer)
- −3
- 3
- −7
Correct answer: 7
In slope-intercept form y = mx + b, b is the y-intercept. Here b = 7.
Question 6: If −4 < 2x ≤ 8, which of the following is a valid solution set for x?
- −2 < x ≤ 4 (Correct answer)
- −8 < x ≤ 16
- −2 ≤ x < 4
- −4 < x ≤ 4
Correct answer: −2 < x ≤ 4
Divide all parts of the compound inequality by 2: −4/2 < 2x/2 ≤ 8/2 → −2 < x ≤ 4.
Math Linear Equations, Inequalities, and Systems
Solve for x: 3(x − 2) + 4 = 2x + 7