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Unit 2 of 5

Unit 2: Equations and Inequalities

Study guide for CLEP CLEP College Algebra — Unit 2: Equations and Inequalities. Practice questions, key concepts, and exam tips.

37

Practice Questions

40

Flashcards

5

Key Topics

Key Concepts to Study

linear equations
quadratic equations
systems of equations
compound inequalities
absolute value equations

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 37.

Q1EASY

Solve the inequality 3x - 2 > 5

A) x < 7/3
B) x > 2
C) x > 7/3
D) x > 1
E) x < 1
Show Answer

Answer: C — x > 7/3 is correct because adding 2 and dividing by 3 gives x > (5 + 2)/3 = 7/3.

Q2MEDIUM

Solve (x+1)/3 + (x-2)/4 = 5/12 for x.

A) x = 7
B) x = 11
C) x = 5
D) x = 1
E) x = -1
Show Answer

Answer: D — x = 1 is correct because to solve (x+1)/3 + (x-2)/4 = 5/12, first find a common denominator for the fractions, which is 12. Multiply both sides of the equation by 12 to clear the fractions: 4(x+1) + 3(x-2) = 5. This simplifies to 4x + 4 + 3x - 6 = 5. Combine like terms: 7x - 2 = 5. Add 2 to both sides: 7x = 7. Divide by 7: x = 1. Thus, x = 1

Q3MEDIUM

Solve |x - 2| = 5

A) x = -1 or x = 5
B) x = -2 or x = 6
C) x = -3 or x = 7
D) x = 1 or x = 3
E) x = 0 or x = 4
Show Answer

Answer: C — x = -3 or x = 7 is correct because |x - 2| = 5 implies x - 2 = ±5, so x = -3 or x = 7.

Q4MEDIUM

Solve for x: |x - 2| = 7

A) x = 2 or x = 7
B) x = -5 or x = -9
C) x = 5 or x = 9
D) x = -9 or x = 5
E) x = -5 or x = 9
Show Answer

Answer: E — x = -5 or x = 9 is correct because |x - 2| = 7 means x - 2 = 7 or x - 2 = -7, so x = 9 or x = -5.

Q5MEDIUM

What is the solution set of |x - 2| = 5?

A) {-2, 6}
B) {-1, 4}
C) {-5, 5}
D) {-7, 3}
E) {-3, 7}
Show Answer

Answer: E — "{-3, 7}" is correct because x - 2 = ±5, yielding x = -3 or x = 7.

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Study Tips for Unit 2: Equations and Inequalities

  • Focus on understanding concepts, not memorizing facts — CLEP tests application
  • Practice with timed questions to build exam-day speed
  • Review explanations for wrong answers — they reveal common misconceptions
  • Use flashcards for key terms, practice questions for deeper understanding

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