COLLEGE ALGEBRA FINAL EXAM 2026 – 200+ Q&AS WITH STEP-BY-STEP RATIONALES (GRADED A+)

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COLLEGE ALGEBRA – EXAM

3|QUESTIONS AND ANSWERS|GRADED

A+|2026 UPDATE|100% CORRECT

1. Solve the linear equation: 3(x−4)=2x+53(x−4)=2x+5

a. x=17x=17

b. x=7x=7

c. x=−7x=−7

d. x=−17x=−17

Answer: a. x=17x=17

Rationale: 3x−12=2x+53x−12=2x+5 → 3x−2x=5+123x−2x

=5+12 → x=17x=17.

2. Solve the quadratic equation by

factoring: x2−5x+6=0x2−5x+6=0

a. x=−2,−3x=−2,−3

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b. x=2,3x=2,3

c. x=−1,−6x=−1,−6

d. x=1,6x=1,6

Answer: b. x=2,3x=2,3

Rationale: Factors to (x−2)(x−3)=0(x−2)(x−3)=0,

so x=2x=2 or x=3x=3.

3. Use the quadratic formula to

solve 2x2+3x−5=02x2+3x−5=0.

a. x=1,−52x=1,−25

b. x=−1,52x=−1,25

c. x=−3±494x=4−3±49

d. Both a and c

Answer: d. Both a and c

Rationale: Quadratic

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formula: x=−3±9−4(2)(−5)4=−3±494=−3±74x=4−3±9−4(2)(

−5)=4−3±49=4−3±7, giving x=1x=1 and x=−52x=−25.

4. Solve the absolute value equation: ∣2x−1∣=7∣2x−1∣=7

a. x=4,−3x=4,−3

b. x=4,3x=4,3

c. x=−4,3x=−4,3

d. x=4,−4x=4,−4

Answer: a. x=4,−3x=4,−3

Rationale: 2x−1=72x−1=7 → x=4x=4;

or 2x−1=−72x−1=−7 → 2x=−62x=−6 → x=−3x=−3.

5. Solve the inequality: 2x+5>92x+5>9

a. x>2x>2

b. x<2x<2

c. x>7x>7

d. x<−2x<−2

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Answer: a. x>2x>2

Rationale: 2x>42x>4 → x>2x>2.

6. Solve the compound inequality: −3≤2x+1<5−3≤2x+1<5

a. −2≤x<2−2≤x<2

b. −4≤x<4−4≤x<4

c. −1≤x<3−1≤x<3

d. −2≤x≤2−2≤x≤2

Answer: a. −2≤x<2−2≤x<2

Rationale: Subtract 1: −4≤2x<4−4≤2x<4; divide by

2: −2≤x<2−2≤x<2.

7. Solve the quadratic inequality: x2−4x+3≤0x2−4x+3≤0

a. 1≤x≤31≤x≤3

b. x≤1x≤1 or x≥3x≥3

c. −3≤x≤−1−3≤x≤−1

d. x≤−3x≤−3 or x≥−1x≥−1