which number line represents the solutions to $-2|x| = -6$?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Inequalities", "Number Line Representation" ], "new_concepts": [ "Absolute Value Equations" ], "current_concepts": [ "Absolute Value Equations", "Number Line Representation" ] } ## Isolate the absolute value expression Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} -2|x| &= -6 \ |x| &= \frac{-6}{-2} \ |x| &= 3 \end{aligned} $$ ## Solve the absolute value equation Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} x = 3 \quad \text{or} \quad x = -3 \end{aligned} $$ ## Represent the solutions on a number line Using the *Number Line Representation* knowledge point $$ \begin{aligned} &\text{Plot solid dots at } x = -3 \text{ and } x = 3. \end{aligned} $$

(A) Number line with solid dots at $-6$ and $-2$

(B) Number line with solid dots at $-8$ and $-4$

(C) Number line with solid dots at $-4$ and $4$

(D) Number line with solid dots at $-3$ and $3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Equations" ] }

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Question

Explanation:

Isolate the absolute value expression

Solve the absolute value equation

Represent the solutions on a number line

Answer: