MATH 110 Module 2 Exam College Algebra & Quantitative
Reasoning Actual Exam 2026/2027 – Complete Questions with
Detailed Rationales | 100% Verified | Pass Guaranteed – A+
Graded
Section A: Linear Equations, Inequalities & Absolute Value
Q1: Solve for x: 3(x − 2) − 4 = 2x + 5
A. x = −7
B. x = 7
C. x = 15 [CORRECT]
D. x = −15
Correct Answer: C
Rationale: Distributing gives 3x − 6 − 4 = 2x + 5, so 3x − 10 = 2x + 5, and subtracting 2x
then adding 10 yields x = 15. Choice B results from adding incorrectly; choice A reverses
the sign.
Q2: Solve the inequality and express the answer in interval notation: −3x + 6 > 12
A. (−2, ∞)
B. (−∞, 2)
C. [−2, ∞)
D. (−∞, −2) [CORRECT]
Correct Answer: D
Rationale: Subtracting 6 gives −3x > 6, and dividing by a negative number reverses the
inequality: x < −2, which is (−∞, −2). Choices A and B fail to flip the inequality sign when
dividing by −3.
Q3: Solve: |2x − 5| = 7
A. x = 6 only
B. x = −1 only
C. x = 6 and x = −1 [CORRECT]
D. No solution
Correct Answer: C
, Rationale: The absolute value equation splits into 2x − 5 = 7 (giving x = 6) and 2x − 5 =
−7 (giving x = −1). Choices A and B each capture only one branch of the equation.
Q4: Solve and graph the solution in interval notation: |x − 3| ≤ 4
A. (−∞, −1] ∪ [7, ∞)
B. (−1, 7)
C. [−7, 1]
D. [−1, 7] [CORRECT]
Correct Answer: D
Rationale: The inequality converts to −4 ≤ x − 3 ≤ 4, so adding 3 throughout gives −1 ≤ x
≤ 7, written [−1, 7] with brackets since "or equal to" is included. Choice A is the correct
interval for |x − 3| ≥ 4, and B uses wrong endpoint inclusion.
Q5: A phone plan charges a $30 monthly base fee plus $0.10 per minute of use. If
Amanda's monthly budget for the plan is $50, which inequality represents the number of
minutes m she can use, and what is the maximum number of minutes?
A. 30 + 0.10m ≤ 50; 200 minutes [CORRECT]
B. 30 + 0.10m ≥ 50; 500 minutes
C. 30m + 0.10 ≤ 50; about 1.7 minutes
D. 0.10m ≤ 30; 300 minutes
Correct Answer: A
Rationale: The cost model is base fee plus per-minute charge: 30 + 0.10m ≤ 50, so
0.10m ≤ 20 and m ≤ 200 minutes. Choice B misuses ≥ and miscomputes; choices C and
D set up the cost structure incorrectly.
Q6: Solve for x: (2x − 1)/3 = (x + 4)/2
A. x = 2
B. x = 10
C. x = −14
D. x = 14 [CORRECT]
Correct Answer: D
Rationale: Cross-multiplying gives 2(2x − 1) = 3(x + 4), so 4x − 2 = 3x + 12, and
subtracting 3x then adding 2 yields x = 14. Choice C results from a sign error, and B
from an arithmetic slip in combining like terms.
Reasoning Actual Exam 2026/2027 – Complete Questions with
Detailed Rationales | 100% Verified | Pass Guaranteed – A+
Graded
Section A: Linear Equations, Inequalities & Absolute Value
Q1: Solve for x: 3(x − 2) − 4 = 2x + 5
A. x = −7
B. x = 7
C. x = 15 [CORRECT]
D. x = −15
Correct Answer: C
Rationale: Distributing gives 3x − 6 − 4 = 2x + 5, so 3x − 10 = 2x + 5, and subtracting 2x
then adding 10 yields x = 15. Choice B results from adding incorrectly; choice A reverses
the sign.
Q2: Solve the inequality and express the answer in interval notation: −3x + 6 > 12
A. (−2, ∞)
B. (−∞, 2)
C. [−2, ∞)
D. (−∞, −2) [CORRECT]
Correct Answer: D
Rationale: Subtracting 6 gives −3x > 6, and dividing by a negative number reverses the
inequality: x < −2, which is (−∞, −2). Choices A and B fail to flip the inequality sign when
dividing by −3.
Q3: Solve: |2x − 5| = 7
A. x = 6 only
B. x = −1 only
C. x = 6 and x = −1 [CORRECT]
D. No solution
Correct Answer: C
, Rationale: The absolute value equation splits into 2x − 5 = 7 (giving x = 6) and 2x − 5 =
−7 (giving x = −1). Choices A and B each capture only one branch of the equation.
Q4: Solve and graph the solution in interval notation: |x − 3| ≤ 4
A. (−∞, −1] ∪ [7, ∞)
B. (−1, 7)
C. [−7, 1]
D. [−1, 7] [CORRECT]
Correct Answer: D
Rationale: The inequality converts to −4 ≤ x − 3 ≤ 4, so adding 3 throughout gives −1 ≤ x
≤ 7, written [−1, 7] with brackets since "or equal to" is included. Choice A is the correct
interval for |x − 3| ≥ 4, and B uses wrong endpoint inclusion.
Q5: A phone plan charges a $30 monthly base fee plus $0.10 per minute of use. If
Amanda's monthly budget for the plan is $50, which inequality represents the number of
minutes m she can use, and what is the maximum number of minutes?
A. 30 + 0.10m ≤ 50; 200 minutes [CORRECT]
B. 30 + 0.10m ≥ 50; 500 minutes
C. 30m + 0.10 ≤ 50; about 1.7 minutes
D. 0.10m ≤ 30; 300 minutes
Correct Answer: A
Rationale: The cost model is base fee plus per-minute charge: 30 + 0.10m ≤ 50, so
0.10m ≤ 20 and m ≤ 200 minutes. Choice B misuses ≥ and miscomputes; choices C and
D set up the cost structure incorrectly.
Q6: Solve for x: (2x − 1)/3 = (x + 4)/2
A. x = 2
B. x = 10
C. x = −14
D. x = 14 [CORRECT]
Correct Answer: D
Rationale: Cross-multiplying gives 2(2x − 1) = 3(x + 4), so 4x − 2 = 3x + 12, and
subtracting 3x then adding 2 yields x = 14. Choice C results from a sign error, and B
from an arithmetic slip in combining like terms.
