Unit 2 of 5
Study guide for CLEP CLEP College Algebra — Unit 2: Equations and Inequalities. Practice questions, key concepts, and exam tips.
30
Practice Questions
41
Flashcards
5
Key Topics
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Solve (x+1)/3 + (x-2)/4 = 5/12 for x.
x = 7
x = 11
x = 5
x = 1
x = -1
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
Solve |x - 2| = 5
x = -1 or x = 5
x = -2 or x = 6
x = -3 or x = 7
x = 1 or x = 3
x = 0 or x = 4
Answer: C — x = -3 or x = 7 is correct because |x - 2| = 5 implies x - 2 = ±5, so x = -3 or x = 7.
Solve for x: |x - 2| = 7
x = 2 or x = 7
x = -5 or x = -9
x = 5 or x = 9
x = -9 or x = 5
x = -5 or x = 9
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.
What is the solution set of |x - 2| = 5?
{-2, 6}
{-1, 4}
{-5, 5}
{-7, 3}
{-3, 7}
Answer: E — "{-3, 7}" is correct because x - 2 = ±5, yielding x = -3 or x = 7.
What is the solution set for the inequality - 4x - 5 < 0?
-1 < x < 5
x < 5 or x > -1
x > -1 and x < 5
x > 5 or x < -1
x < -1 or x > 5
Answer: A — -1 < x < 5 is correct because factoring gives (x - 5)(x + 1) < 0, so -1 < x < 5..
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