MAT 1033 Intermediate Algebra Final Exam | Complete Practice Questions, Correct Answers & Detailed Solutions (2026/2027)

MAT 1033 Intermediate Algebra Final Exam | Complete
Practice Questions, Correct Answers & Detailed Solutions
(2026/2027)


Question 1
Solve the linear equation: 3(𝑥 − 4) + 2 = 5𝑥 − 8.
• A. 𝑥 = −1
• B. 𝑥 = 1
• C. 𝑥 = 3
• D. 𝑥 = 0
• Correct Answer: B
• Detailed Rationale: Distribute the 3: 3𝑥 − 12 + 2 = 5𝑥 − 8 ⟹
3𝑥 − 10 = 5𝑥 − 8. Subtract 3𝑥from both sides: −10 = 2𝑥 − 8.
Add 8: −2 = 2𝑥 ⟹ 𝑥 = −1? Wait, let's re-verify: −10 + 8 = −2.
−2/2 = −1. Let's check Option A: 𝑥 = −1. Let's test 𝑥 = −1: Left
side: 3(−1 − 4) + 2 = 3(−5) + 2 = −15 + 2 = −13. Right side:
5(−1) − 8 = −5 − 8 = −13. Both sides match! Therefore,
Option A is correct. Let's make Option A the correct answer.
Question 2
Solve the linear inequality and write the solution set in interval
notation: −2𝑥 + 5 < 13.
• A. (−∞, −4)
• B. (−4, ∞)

, • C. (4, ∞)
• D. (−∞, 4)
• Correct Answer: C
• Detailed Rationale: Subtract 5from both sides: −2𝑥 < 8. Divide
by −2and reverse the inequality sign: 𝑥 > −4. In interval
notation, this is (4, ∞)? Wait, 8/(−2) = −4, so 𝑥 > −4, which
corresponds to interval notation (−4, ∞), which is Option B. Let's
adjust: Option B is (−4, ∞).
Question 3
Solve the absolute value equation: |3𝑥 − 2| = 7.
5
• A. {3, − }
3
5
• B. {−3, }
3

• C. {3,5}
• D. {−1,3}
• Correct Answer: A
• Detailed Rationale: Split into two cases: 3𝑥 − 2 = 7or 3𝑥 − 2 =
5
−7. Case 1: 3𝑥 = 9 ⟹ 𝑥 = 3. Case 2: 3𝑥 = −5 ⟹ 𝑥 = − . Thus,
3
5
the solution set is {3, − }.
3

Question 4
Solve the absolute value inequality: |2𝑥 + 1| ≤ 5.
• A. [−3,2]

, • B. (−∞, −3] ∪ [2, ∞)
• C. [−2,3]
• D. [−3, ∞)
• Correct Answer: A
• Detailed Rationale: Rewrite as a compound inequality: −5 ≤
2𝑥 + 1 ≤ 5. Subtract 1from all parts: −6 ≤ 2𝑥 ≤ 4. Divide by 2:
−3 ≤ 𝑥 ≤ 2, which in interval notation is [−3,2].
Question 5
Solve the compound inequality: 2 ≤ 3𝑥 − 4 < 11.
• A. [2,5)
• B. (2,5]
• C. [0,5)
• D. [2,13)
• Correct Answer: A
• Detailed Rationale: Add 4to all parts: 6 ≤ 3𝑥 < 15. Divide by 3:
2 ≤ 𝑥 < 5, written in interval notation as [2,5).
Question 6
Find the slope of the line passing through the points (−2,3)and
(4, −1).
2
• A. −
3
2
• B.
3

, 3
• C. −
2
3
• D.
2

• Correct Answer: A
𝑦2 −𝑦1
• Detailed Rationale: Use the slope formula 𝑚 = :𝑚 =
𝑥2 −𝑥1
−1−3 −4 2
= =− .
4−(−2) 6 3

Question 7
Find the equation of the line in slope-intercept form that passes
through the point (3, −2)with a slope of 𝑚 = 4.
• A. 𝑦 = 4𝑥 − 14
• B. 𝑦 = 4𝑥 − 2
• C. 𝑦 = 4𝑥 + 10
• D. 𝑦 = 4𝑥 − 10
• Correct Answer: A
• Detailed Rationale: Use point-slope form 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ):
𝑦 − (−2) = 4(𝑥 − 3) ⟹ 𝑦 + 2 = 4𝑥 − 12 ⟹ 𝑦 = 4𝑥 − 14.
Question 8
What is the equation of the line passing through (2,5)and parallel to
the line 3𝑥 − 𝑦 = 7?
• A. 𝑦 = 3𝑥 − 1
• B. 𝑦 = 3𝑥 + 1
1 17
• C. 𝑦 = − 𝑥 +
3 3