solve the following compound inequality. $\frac{m - 2}{3} 15$ $m $

Question

solve the following compound inequality. $\frac{m - 2}{3} < -2$ or $4m + 3 > 15$ $m < ?$ or $m > $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Solving Inequalities" ], "new_concepts": [ "Compound Inequalities" ], "current_concepts": [ "Solving Inequalities", "Compound Inequalities" ] } ## Solve the first inequality Using the *Solving Inequalities* knowledge point $$ \begin{aligned} \frac{m - 2}{3} &< -2 \ m - 2 &< -6 \ m &< -4 \end{aligned} $$ ## Solve the second inequality Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 4m + 3 &> 15 \ 4m &> 12 \ m &> 3 \end{aligned} $$ ## Combine the solutions We combine the individual solutions using the logical operator "OR" to form the final compound inequality. $$ m < -4 \quad \text{OR} \quad m > 3 $$ Solve the following compound inequality. $$\frac{m - 2}{3} < -2 \text{ OR } 4m + 3 > 15$$ $m <$ -4 $\text{ OR } m >$ 3 { "elements": [ { "type": "bentinequality", "params": [{ "x": -4, "operator": "<", "labelText": "m < -4", "strokeColor": "#8C55F2", "strokeWidth": 3 }] }, { "type": "bentinequality", "params": [{ "x": 3, "operator": ">", "labelText": "m > 3", "strokeColor": "#5583F2", "strokeWidth": 3 }] } ], "timestamps": [0.1, 0.5] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Compound Inequalities" ] }

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Question

Explanation:

Solve the first inequality

Solve the second inequality

Combine the solutions

Answer: