select the correct answer.

which inequality is represented by this number line?

$|2x + 1| \ge 7$

$2|x + 1| \le 8$

$|2x - 1| \ge 9$

$2|x - 1| \le 10$

Question

select the correct answer.

which inequality is represented by this number line?

$|2x + 1| \ge 7$

$2|x + 1| \le 8$

$|2x - 1| \ge 9$

$2|x - 1| \le 10$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Inequalities" ], "new_concepts": [], "current_concepts": [ "Absolute Value Inequalities", "Solving Compound Inequalities" ] } ## Identify the interval from the number line $$ x \le -4 \quad \text{or} \quad x \ge 5 $$ ## Find the midpoint and distance $$ \begin{aligned} &\text{Midpoint} = \frac{-4 + 5}{2} = 0.5\ &\text{Distance} = \frac{5 - (-4)}{2} = 4.5 \end{aligned} $$ ## Formulate the absolute value inequality $$ \begin{aligned} &|x - 0.5| \ge 4.5\ &|2x - 1| \ge 9 \end{aligned} $$

(A) $|2x + 1| \ge 7$

(B) $2|x + 1| \le 8$

(C) $|2x - 1| \ge 9$

(D) $2|x - 1| \le 10$

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

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QUESTION IMAGE

Question

Explanation:

Identify the interval from the number line

Find the midpoint and distance

Formulate the absolute value inequality

Answer: