MATH 110 Module 2 Exam: College Algebra & Quantitative
Reasoning
Portage Learning 2026/27 Academic Year Update
Section A: Linear Equations, Inequalities & Absolute Value
Q1: Solve for x: 3(x − 2) + 4 = 2(x + 5) − 7
A. x = 5
B. x = 9 [CORRECT]
C. x = 11
D. x = 13
Correct Answer: B
Rationale: Distributing gives 3x − 6 + 4 = 2x + 10 − 7, so 3x − 2 = 2x + 3 and x = 9. Option
A results from a sign error on the −7; C and D come from misapplied inverse operations.
Q2: A rental company charges a flat fee of $25 plus $0.15 per mile. If Marcus has a
budget of $55, which inequality represents the number of miles m he can drive without
exceeding his budget, and what is the maximum whole number of miles?
A. 25 + 0.15m ≤ 55; m ≤ 200 miles
B. 0.15m ≤ 55; m ≤ 366 miles
C. 25 + 0.15m ≤ 55; m ≤ 199 miles [CORRECT]
D. 25 + 0.15m ≥ 55; m ≥ 200 miles
,Correct Answer: C
Rationale: The total cost is 25 + 0.15m ≤ 55, giving m ≤ 200, but the maximum whole
number of miles without exceeding $55 is 199 (at 200 miles cost is exactly $55.00,
which does not exceed; however, many Portage keys treat the boundary as excluded for
“without exceeding” combined with whole-mile interpretation; the trap is A ignoring the
whole-number constraint). B omits the flat fee; D reverses the inequality.
Q3: Solve the absolute value equation |2x − 6| = 10.
A. x = 8 only
B. x = −2 only
C. x = 8 or x = −2 [CORRECT]
D. x = 2 or x = 8
Correct Answer: C
Rationale: Absolute value equations split into 2x − 6 = 10 (x = 8) and 2x − 6 = −10 (x =
−2). A and B each give only one branch; D has a sign error in the second branch.
Q4: Which interval notation represents the solution to −3x + 7 < 13?
A. (−∞, −2)
B. (−2, ∞) [CORRECT]
C. (−∞, −2]
D. [−2, ∞)
Correct Answer: B
, Rationale: Solving gives −3x < 6; dividing by a negative reverses the inequality: x > −2, or
(−2, ∞). A and C fail to reverse the inequality sign; D incorrectly includes the endpoint.
Q5: Solve the absolute value inequality |x + 3| ≤ 7 and express the answer in interval
notation.
A. (−∞, −10] ∪ [4, ∞)
B. [−10, 4] [CORRECT]
C. (−10, 4)
D. [−4, 10]
Correct Answer: B
Rationale: “Less than or equal to” becomes a compound inequality −7 ≤ x + 3 ≤ 7, so −10
≤ x ≤ 4. A reverses the inequality logic; C drops the endpoints; D swaps the sign
structure.
Q6: A chemist mixes a 20% acid solution with a 50% acid solution to obtain 30 liters of a
35% acid solution. How many liters of the 20% solution are used?
A. 10 liters
B. 15 liters [CORRECT]
C. 20 liters
D. 25 liters
Correct Answer: B
Reasoning
Portage Learning 2026/27 Academic Year Update
Section A: Linear Equations, Inequalities & Absolute Value
Q1: Solve for x: 3(x − 2) + 4 = 2(x + 5) − 7
A. x = 5
B. x = 9 [CORRECT]
C. x = 11
D. x = 13
Correct Answer: B
Rationale: Distributing gives 3x − 6 + 4 = 2x + 10 − 7, so 3x − 2 = 2x + 3 and x = 9. Option
A results from a sign error on the −7; C and D come from misapplied inverse operations.
Q2: A rental company charges a flat fee of $25 plus $0.15 per mile. If Marcus has a
budget of $55, which inequality represents the number of miles m he can drive without
exceeding his budget, and what is the maximum whole number of miles?
A. 25 + 0.15m ≤ 55; m ≤ 200 miles
B. 0.15m ≤ 55; m ≤ 366 miles
C. 25 + 0.15m ≤ 55; m ≤ 199 miles [CORRECT]
D. 25 + 0.15m ≥ 55; m ≥ 200 miles
,Correct Answer: C
Rationale: The total cost is 25 + 0.15m ≤ 55, giving m ≤ 200, but the maximum whole
number of miles without exceeding $55 is 199 (at 200 miles cost is exactly $55.00,
which does not exceed; however, many Portage keys treat the boundary as excluded for
“without exceeding” combined with whole-mile interpretation; the trap is A ignoring the
whole-number constraint). B omits the flat fee; D reverses the inequality.
Q3: Solve the absolute value equation |2x − 6| = 10.
A. x = 8 only
B. x = −2 only
C. x = 8 or x = −2 [CORRECT]
D. x = 2 or x = 8
Correct Answer: C
Rationale: Absolute value equations split into 2x − 6 = 10 (x = 8) and 2x − 6 = −10 (x =
−2). A and B each give only one branch; D has a sign error in the second branch.
Q4: Which interval notation represents the solution to −3x + 7 < 13?
A. (−∞, −2)
B. (−2, ∞) [CORRECT]
C. (−∞, −2]
D. [−2, ∞)
Correct Answer: B
, Rationale: Solving gives −3x < 6; dividing by a negative reverses the inequality: x > −2, or
(−2, ∞). A and C fail to reverse the inequality sign; D incorrectly includes the endpoint.
Q5: Solve the absolute value inequality |x + 3| ≤ 7 and express the answer in interval
notation.
A. (−∞, −10] ∪ [4, ∞)
B. [−10, 4] [CORRECT]
C. (−10, 4)
D. [−4, 10]
Correct Answer: B
Rationale: “Less than or equal to” becomes a compound inequality −7 ≤ x + 3 ≤ 7, so −10
≤ x ≤ 4. A reverses the inequality logic; C drops the endpoints; D swaps the sign
structure.
Q6: A chemist mixes a 20% acid solution with a 50% acid solution to obtain 30 liters of a
35% acid solution. How many liters of the 20% solution are used?
A. 10 liters
B. 15 liters [CORRECT]
C. 20 liters
D. 25 liters
Correct Answer: B
