Week 2 — Quiz (auto-graded) · Linear Equations & Inequalities

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective tested: Objective 2 — solving linear equations, linear inequalities (interval notation), absolute-value equations and inequalities.
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 2.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-02-qti.xml. AI is not permitted on quizzes (course AI policy). Every numeric answer below is pre-computed and independently re-verified (Python w02_verify.py, PASS).

Blueprint

No trick questions; distractors target the Week 2 misconceptions named in the lecture outline (forgotten sign flip, |x|=−5 trap, "and"/"or" confusion for AV inequalities, identity misclassification).

Questions, key, and feedback

Q1 (MC). Solve: 3(x − 2) = 2x + 5
- A. x = 3
- B. x = 5
- C. x = 8
- D. x = 11 ✅
Feedback: Distribute: 3x − 6 = 2x + 5. Subtract 2x: x − 6 = 5. Add 6: x = 11. (A came from not distributing the 3; B is 3+2 instead of solving; C came from a subtraction error.)

Q2 (MC). Solve: x/2 + 1/3 = 5/6
- A. x = 1 ✅
- B. x = 2
- C. x = 3/5
- D. x = 5/3
Feedback: LCD = 6. Multiply every term: 3x + 2 = 5 → 3x = 3 → x = 1. Check: 1/2 + 1/3 = 3/6 + 2/6 = 5/6 ✓. (B from adding fractions without finding LCD; C/D from fraction arithmetic errors.)

Q3 (MC). Solve: −2x + 1 < 9. Write the solution in interval notation.
- A. (−∞, −4)
- B. (−4, ∞) ✅
- C. (4, ∞)
- D. (−∞, 4)
Feedback: Subtract 1: −2x < 8. Divide by −2 — negative divisor, flip the sign — x > −4. Interval: (−4, ∞). (A is x < −4, forgetting to flip; C and D have the wrong boundary value.)

Q4 (Matching). Match each inequality to its interval notation.
| Inequality | Interval |
|---|---|
| x > −4 | (−4, ∞) |
| x ≤ 3 | (−∞, 3] |
| −1 < x ≤ 2 | (−1, 2] |
| x ≥ 0 | [0, ∞) |
Feedback: Strict inequality (< or >) → parenthesis; non-strict (≤ or ≥) → bracket. Infinity always gets a parenthesis. The mixed interval −1 < x ≤ 2 has a parenthesis on the left (−1 excluded) and a bracket on the right (2 included).

Q5 (MC). Solve: |x| = 7
- A. x = 7 only
- B. x = −7 only
- C. No solution
- D. x = 7 or x = −7 ✅
Feedback: Since 7 > 0, the equation has two solutions: x = 7 and x = −7. Both are distance 7 from zero. (A and B each miss one solution; C would apply only if the right side were negative.)

Q6 (MC). Solve: |2x − 1| = 7
- A. x = 3 or x = −4
- B. x = 4 or x = −3 ✅
- C. x = 4 only
- D. x = −4 or x = 3
Feedback: Case 1: 2x − 1 = 7 → 2x = 8 → x = 4. Case 2: 2x − 1 = −7 → 2x = −6 → x = −3. Check: |2(4)−1| = 7 ✓; |2(−3)−1| = |−7| = 7 ✓. (A/D reflect sign errors in one or both cases.)

Q7 (MC). Solve: |x| < 5. Write the solution in interval notation.
- A. (−∞, −5) ∪ (5, ∞)
- B. (−5, 5) ✅
- C. [−5, 5]
- D. (5, ∞)
Feedback: "Less than" absolute value → AND → middle interval: −5 < x < 5 → (−5, 5). (A is the "greater than" case; C uses brackets (but 5 and −5 are not included); D is only the positive tail.)

Q8 (MC). Solve: |x| ≥ 3. Write the solution in interval notation.
- A. (−3, 3)
- B. [−3, 3]
- C. (−∞, −3] ∪ [3, ∞) ✅
- D. (−∞, −3) ∪ (3, ∞)
Feedback: "Greater than or equal" absolute value → OR → two outer rays: x ≤ −3 or x ≥ 3 → (−∞, −3] ∪ [3, ∞). (A and B are the middle-interval shape, which belongs to the "less than" case; D is missing the brackets at ±3.)

Q9 (True / False). "2(x + 3) = 2x + 6 has exactly one solution."
- True
- False ✅
Feedback: False. Simplify: 2x + 6 = 2x + 6 → 0 = 0. This is true for every real number — an identity with infinitely many solutions. "Exactly one solution" is the classic misconception when students see 0 = 0 and don't recognize an identity.*

Q10 (MC). A taxi charges a $3 base fee plus $2 per mile. If a ride costs $15, how many miles was the ride?
- A. 4 miles
- B. 5 miles
- C. 6 miles ✅
- D. 9 miles
Feedback: Equation: 3 + 2m = 15 → 2m = 12 → m = 6. Check: 3 + 2(6) = 3 + 12 = 15 ✓. (A = 4 forgets the +3 flat fee and divides 15 by… or subtracts twice; B = 5 divides 15 by 3 only; D = 9 subtracts 2m the wrong way. All reflect setup/arithmetic slips that miss m = 6.)

Answer key (quick reference)

Quality gate (self-checked, computer-verified): each single-answer item has exactly one correct option; the matching item pairs all four inequalities one-to-one with their interval-notation forms; no multi-answer items this week. Arithmetic pre-computed and independently re-verified (w02_verify.py, PASS): Q1 3(11−2)=27=2(11)+5 ✓; Q2 1/2+1/3=5/6 ✓; Q3 −2(−4)+1=9 boundary check ✓; Q5 |7|=7 ✓, |−7|=7 ✓; Q6 |7|=7 ✓, |−7|=7 ✓; Q7 |±4.9|<5 ✓, boundary excluded ✓; Q8 |±3|≥3 ✓, boundary included ✓; Q9 identity confirmed (0=0); Q10 3+2(6)=15 ✓. All checks PASS. QTI parse confirmation: F-quiz-week-02-qti.xml parses as imsqti_xmlv1p2 with 10 items.

Item-bank entries (for variants + the midterm/final)

All ten items are tagged course=MATH120 · week=2 · objective=2 · topic=linear-equations-inequalities-absolute-value and deposited in Item Bank: Week 2 — Linear Equations & Inequalities. The midterm (Week 8) and per-term variant updates draw from this bank. (Tags: q1 linear-eqn-distribute, q2 linear-eqn-fractions, q3 inequality-sign-flip, q4 interval-notation-matching, q5 abs-val-eqn-basic, q6 abs-val-eqn-expression, q7 abs-val-ineq-less-than, q8 abs-val-ineq-greater-than, q9 identity-tf, q10 application-linear.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 2 Quiz — Linear Equations & Inequalities"
assignment_group = "Quizzes"
points_possible = 10
grading_type    = points
due_offset_days = 6        # 6 days after module start (module starts Tue Sep 8)
published       = true
shuffle_answers = true
provenance      = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"