solve the inequality $\frac{2}{3}x - \frac{5}{6} \ge \frac{1}{2}$. which number line represents the graph of the solution?

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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": [ "Solving Inequalities", "Inequality Graphing" ], "new_concepts": [], "current_concepts": [ "Solving Inequalities", "Inequality Graphing" ] } ## Solve the inequality for x $$ \begin{aligned} \frac{2}{3}x - \frac{5}{6} &\ge \frac{1}{2} \ \frac{2}{3}x &\ge \frac{1}{2} + \frac{5}{6} \ \frac{2}{3}x &\ge \frac{3}{6} + \frac{5}{6} \ \frac{2}{3}x &\ge \frac{8}{6} \ \frac{2}{3}x &\ge \frac{4}{3} \end{aligned} $$ ## Isolate the variable x $$ \begin{aligned} x &\ge \frac{4}{3} \cdot \frac{3}{2} \ x &\ge 2 \end{aligned} $$ ## Identify the matching number line graph $$ \begin{aligned} &\text{The inequality } x \ge 2 \text{ is represented by:} \ &\text{- A solid circle at } 2 \ &\text{- A shaded arrow pointing to the right} \end{aligned} $$

(A) Solid circle at 12, shaded to the right

(B) Solid circle at 2, shaded to the right

(C) Solid circle at $-\frac{1}{2}$, shaded to the right

(D) Solid circle at $-\frac{2}{9}$, shaded to the right

{ "elements": [ { "type": "line", "params": [[-5, 0], [5, 0]], "properties": { "strokeColor": "#583C87", "strokeWidth": 2, "fixed": true } }, { "type": "arrow", "params": [[2, 0], [5, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 4 } }, { "type": "point", "params": [[2, 0]], "properties": { "name": "2", "size": 5, "strokeColor": "#8C55F2", "fillColor": "#8C55F2", "withLabel": true, "labelPosition": [0, -15] } }, { "type": "point", "params": [[-2, 0]], "properties": { "name": "-2", "size": 2, "strokeColor": "#583C87", "fillColor": "#583C87", "withLabel": true, "labelPosition": [0, -15] } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "0", "size": 2, "strokeColor": "#583C87", "fillColor": "#583C87", "withLabel": true, "labelPosition": [0, -15] } }, { "type": "point", "params": [[4, 0]], "properties": { "name": "4", "size": 2, "strokeColor": "#583C87", "fillColor": "#583C87", "withLabel": true, "labelPosition": [0, -15] } } ], "timestamps": [0.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Inequalities" ] }

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Question

Explanation:

Solve the inequality for x

Isolate the variable x

Identify the matching number line graph

Answer: