2.6 compound inequalities quiz

what graph matches the compound inequality below?

\-2 \le 3x - 8 \le 10\

Question

2.6 compound inequalities quiz

what graph matches the compound inequality below?

\-2 \le 3x - 8 \le 10\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Compound Inequalities" ], "new_concepts": [], "current_concepts": [ "Compound Inequalities", "Solving Inequalities", "Graphing Inequalities" ] } ## Isolate the variable term $$ \begin{aligned} &-2 \le 3x - 8 \le 10 \ &-2 + 8 \le 3x \le 10 + 8 \ &6 \le 3x \le 18 \end{aligned} $$ ## Solve for x $$ \begin{aligned} &\frac{6}{3} \le x \le \frac{18}{3} \ &2 \le x \le 6 \end{aligned} $$ ## Identify the matching graph $$ \begin{aligned} &\text{Interval: } [2, 6] \ &\text{Graph: Closed circles at } 2 \text{ and } 6 \text{ with shading between them.} \end{aligned} $$

(A) Shaded segment between closed circles at 2 and 6

(B) Shaded segment between closed circles at 1 and 6

{ "elements": [ { "type": "line", "params": [[0, 0], [8, 0]], "properties": { "strokeColor": "#583C87", "strokeWidth": 2, "straightFirst": true, "straightLast": true } }, { "type": "point", "params": [[1, 0]], "properties": { "name": "1", "size": 3, "color": "#583C87", "withLabel": true, "fixed": true } }, { "type": "point", "params": [[2, 0]], "properties": { "name": "2", "size": 5, "color": "#8C55F2", "withLabel": true, "fixed": true } }, { "type": "point", "params": [[3, 0]], "properties": { "name": "3", "size": 3, "color": "#583C87", "withLabel": true, "fixed": true } }, { "type": "point", "params": [[4, 0]], "properties": { "name": "4", "size": 3, "color": "#583C87", "withLabel": true, "fixed": true } }, { "type": "point", "params": [[5, 0]], "properties": { "name": "5", "size": 3, "color": "#583C87", "withLabel": true, "fixed": true } }, { "type": "point", "params": [[6, 0]], "properties": { "name": "6", "size": 5, "color": "#8C55F2", "withLabel": true, "fixed": true } }, { "type": "segment", "params": [[2, 0], [6, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 6 } } ], "timestamps": [0.1] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Compound Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the variable term

Solve for x

Identify the matching graph

Answer: