2. which of the following double inequalities represents the inequality $|y - 3| - 4 \le -3$?

$y - 3 \le -1$ or $y - 3 \ge 1$

$-1 \le y - 3$ and $y - 3 \le 1$

$y - 3 \le -1$ and $y - 3 \ge 1$

$-1 \le y - 3$ or $y - 3 \le 1$

Question

2. which of the following double inequalities represents the inequality $|y - 3| - 4 \le -3$?

$y - 3 \le -1$ or $y - 3 \ge 1$

$-1 \le y - 3$ and $y - 3 \le 1$

$y - 3 \le -1$ and $y - 3 \ge 1$

$-1 \le y - 3$ or $y - 3 \le 1$

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", "Compound Inequalities" ] } ## Isolate the absolute value expression Using the **Absolute Value Inequalities** knowledge point $$ \begin{aligned} |y - 3| - 4 &\le -3 \ |y - 3| &\le -3 + 4 \ |y - 3| &\le 1 \end{aligned} $$ ## Rewrite as a compound inequality Using the **Absolute Value Inequalities** knowledge point $$ \begin{aligned} -1 \le y - 3 \le 1 \end{aligned} $$ This compound inequality can be written as two separate inequalities joined by the word "AND": $$ -1 \le y - 3 \quad \text{AND} \quad y - 3 \le 1 $$

(A) $y - 3 \le -1 \text{ OR } y - 3 \ge 1$

(B) $-1 \le y - 3 \text{ AND } y - 3 \le 1$

(C) $y - 3 \le -1 \text{ AND } y - 3 \ge 1$

(D) $-1 \le y - 3 \text{ OR } y - 3 \le 1$

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

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Question

Explanation:

Isolate the absolute value expression

Rewrite as a compound inequality

Answer: