8
QuizMultiple Choice

Quadratic Inequalities — Quiz

Question 8 • Advanced Algebra: Concepts and Connections

What is the solution set to the inequality open paren 4 x minus 3 close paren times open paren 2 x minus 1 close paren is greater than or equal to 0 ?

Answer
A
start set x such that x is less than or equal to 3 or x comma 3 or x is greater than or equal to 1 end set
B
start set x such that x is less than or equal to 1 half or x comma 1 half or x is greater than or equal to 3 fourths end set
C
start set x such that x is less than or equal to negative 1 half or x comma negative 1 half or x is greater than or equal to negative 3 fourths end set
D
start set x such that x is less than or equal to 2 or x comma 2 or x is greater than or equal to 4 thirds end set

Explanation

The factors are zero at x = 3/4 and x = 1/2. Since the product is nonnegative when both factors have the same sign, the solution is x ≤ 1/2 or x ≥ 3/4, including the zeros because the inequality allows equality. This matches choice B: x is less than or equal to 1/2 or greater than or equal to 3/4.

AI-written and checked against the verified answer.

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