what is the solution set to the inequality $5(x - 2)(x + 4) 0$? $\{x \mid x -4 \text{ and } x -2 \text{ or } x

Question

what is the solution set to the inequality \$5(x - 2)(x + 4) > 0\$?

\$\\{x \mid x > -4 \text{ and } x < 2\\}\$
\$\\{x \mid x < -4 \text{ or } x > 2\\}\$
\$\\{x \mid x < -2 \text{ or } x > 4\\}\$
\$\\{x \mid x > -2 \text{ or } x < 4\\}\$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Inequalities" ], "new_concepts": [], "current_concepts": [ "Quadratic Inequalities", "Zeros of Quadratic Functions" ] } ## Find the boundary points of the inequality $$ 5(x - 2)(x + 4) = 0 \implies x = 2 \quad \text{or} \quad x = -4 $$ ## Determine the sign of the quadratic expression on each interval $$ \begin{aligned} &\text{For } x < -4: \quad 5(x - 2)(x + 4) > 0 \quad (\text{Positive}) \ &\text{For } -4 < x < 2: \quad 5(x - 2)(x + 4) < 0 \quad (\text{Negative}) \ &\text{For } x > 2: \quad 5(x - 2)(x + 4) > 0 \quad (\text{Positive}) \end{aligned} $$ ## State the solution set for the strict inequality $$ \{x \mid x < -4 \text{ or } x > 2\} $$

{x | x > -4 and x < 2}

{x | x < -4 or x > 2}

{x | x < -2 or x > 4}

{x | x > -2 or x < 4}

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Inequalities" ] }

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Question

Explanation:

Find the boundary points of the inequality

Determine the sign of the quadratic expression on each interval

State the solution set for the strict inequality

Answer: