2. which graph represents the solution to $|3k - 2| 7$?

Question

2. which graph represents the solution to $|3k - 2| > 7$?

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" ], "new_concepts": [], "current_concepts": [ "Absolute Value Inequalities", "Solving Linear Inequalities", "Graphing Inequalities" ] } ## Set up the compound inequality Using the *Absolute Value Inequalities* knowledge point $$ 3k - 2 > 7 \quad \text{or} \quad 3k - 2 < -7 $$ ## Solve the first inequality Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} 3k - 2 &> 7 \ 3k &> 9 \ k &> 3 \end{aligned} $$ ## Solve the second inequality Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} 3k - 2 &< -7 \ 3k &< -5 \ k &< -\frac{5}{3} \approx -1.67 \end{aligned} $$ ## Identify the correct graph representation Using the *Graphing Inequalities* knowledge point $$ \begin{aligned} &\text{Solution set: } k < -1.67 \quad \text{or} \quad k > 3\ &\text{Graph features: open circles at } -1.67 \text{ and } 3\text{, shaded outwards.} \end{aligned} $$

(A) A number line shaded entirely from -5 to 5.

(B) A number line with open circles at -1.67 and 3, shaded between them.

(C) A number line with open circles at -1.67 and 3, shaded outwards to the left and right.

(D) no solution

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the compound inequality

Solve the first inequality

Solve the second inequality

Identify the correct graph representation

Answer: