solve for the variable in each equation.
1. $3m + 2 = 62$
2. $4x - 7 = -83$
3. $8x + 1 = -55$
4. $\frac{b}{2} - 4 = -7$
5. $\frac{a}{3} - 1 = 1$
6. $-8 = -5 + \frac{m}{3}$

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{ "quality": "clear", "question_count": 6, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Two-Step Equations", "Linear Equations", "Algebraic Isolation" ], "new_concepts": [], "current_concepts": [ "Two-Step Equations", "Linear Equations", "Algebraic Isolation" ] } ## Solve equations 1, 2, and 3 Using the *Two-Step Equations* and *Linear Equations* knowledge points $$ \begin{aligned} &\text{Equation 1: } 3m + 2 = 62 \implies 3m = 60 \implies m = 20\ &\text{Equation 2: } 4x - 7 = -83 \implies 4x = -76 \implies x = -19\ &\text{Equation 3: } 8x + 1 = -55 \implies 8x = -56 \implies x = -7 \end{aligned} $$ ## Solve equations 4, 5, and 6 Using the *Two-Step Equations* and *Algebraic Isolation* knowledge points $$ \begin{aligned} &\text{Equation 4: } \frac{b}{2} - 4 = -7 \implies \frac{b}{2} = -3 \implies b = -6\ &\text{Equation 5: } \frac{a}{3} - 1 = 1 \implies \frac{a}{3} = 2 \implies a = 6\ &\text{Equation 6: } -8 = -5 + \frac{m}{3} \implies -3 = \frac{m}{3} \implies m = -9 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $3m + 2 = 62$ | $m = 20$ | | 2 | $4x - 7 = -83$ | $x = -19$ | | 3 | $8x + 1 = -55$ | $x = -7$ | | 4 | $\frac{b}{2} - 4 = -7$ | $b = -6$ | | 5 | $\frac{a}{3} - 1 = 1$ | $a = 6$ | | 6 | $-8 = -5 + \frac{m}{3}$ | $m = -9$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Two-Step Equations" ] }

No.	Problem	Answer
2	\(4x - 7 = -83\)	\(x = -19\)
3	\(8x + 1 = -55\)	\(x = -7\)
4	\(\frac{b}{2} - 4 = -7\)	\(b = -6\)
5	\(\frac{a}{3} - 1 = 1\)	\(a = 6\)
6	\(-8 = -5 + \frac{m}{3}\)	\(m = -9\)

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Solve equations 1, 2, and 3

Solve equations 4, 5, and 6

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