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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Algebraic Simplification", "Absolute Value Inequalities" ], "new_concepts": [], "current_concepts": [ "Absolute Value Inequalities", "Solving Linear Inequalities", "Algebraic Simplification" ] } ## Isolate the absolute value expression Using the **Algebraic Simplification** knowledge point $$ \begin{aligned} -|x + 3| + 2 &\ge -5 \ -|x + 3| &\ge -7 \ |x + 3| &\le 7 \end{aligned} $$ ## Set up the compound inequality Using the **Absolute Value Inequalities** knowledge point $$ -7 \le x + 3 \le 7 $$ ## Solve for x Using the **Algebraic Simplification** knowledge point $$ \begin{aligned} -7 - 3 &\le x \le 7 - 3 \ -10 &\le x \le 4 \end{aligned} $$

(A) $x \le -10$ or $x \ge 4$

(B) $-10 \le x \le 4$

(C) No solution

(D) $x \le -4$ or $x \ge -2$

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

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Question

Explanation:

Isolate the absolute value expression

Set up the compound inequality

Solve for x

Answer: