which number line represents the solution set for the inequality $-4(x + 3) \le -2 - 2x$?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Solving Linear Inequalities", "Number Line Representation" ], "current_concepts": [ "Solving Linear Inequalities", "Number Line Representation" ] } ## Solve the inequality algebraically $$ \begin{aligned} -4(x + 3) &\le -2 - 2x \ -4x - 12 &\le -2 - 2x \ -12 + 2 &\le -2x + 4x \ -10 &\le 2x \ -5 &\le x \ x &\ge -5 \end{aligned} $$ ## Identify the correct number line representation $$ \begin{aligned} &\text{Boundary point: } x = -5 \text{ (solid circle, since inequality is } \ge\text{)} \ &\text{Direction: to the right (values greater than or equal to } -5\text{)} \end{aligned} $$

(A) Solid circle at -5 with arrow pointing to the right

(B) Solid circle at 5 with arrow pointing to the right

(C) Solid circle at 5 with arrow pointing to the left

(D) Solid circle at -5 with arrow pointing to the left

{ "elements": [ { "type": "line", "params": [[-8, 0], [8, 0]], "properties": { "strokeColor": "#583C87", "strokeWidth": 2, "fixed": true } }, { "type": "point", "params": [[-5, 0]], "properties": { "name": "-5", "size": 4, "color": "#8C55F2", "withLabel": true, "fixed": true } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "0", "size": 2, "color": "#583C87", "withLabel": true, "fixed": true } }, { "type": "point", "params": [[5, 0]], "properties": { "name": "5", "size": 2, "color": "#583C87", "withLabel": true, "fixed": true } }, { "type": "bentinequality", "params": [{ "x": -5, "operator": ">=", "labelText": "x \ge -5", "strokeColor": "#8C55F2", "strokeWidth": 4 }] } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Linear Inequalities" ] }

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Question

Explanation:

Solve the inequality algebraically

Identify the correct number line representation

Answer: