6. solve for the unknown variable in each of the following.
a) $-3a = -15$
b) $b - 6 = 14$
c) $\frac{c}{2} + 6 = 16$
d) $4x - 2 = 10$

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Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Integer Arithmetic" ], "new_concepts": [ "Solving Linear Equations", "One-Step Equations", "Two-Step Equations" ], "current_concepts": [ "Integer Arithmetic", "Solving Linear Equations", "One-Step Equations", "Two-Step Equations" ] } ## Solve equation a $$ \begin{aligned} -3a &= 15 \ a &= \frac{15}{-3} \ a &= -5 \end{aligned} $$ ## Solve equation b $$ \begin{aligned} b - 6 &= 14 \ b &= 14 + 6 \ b &= 20 \end{aligned} $$ ## Solve equation c $$ \begin{aligned} \frac{c}{2} + 6 &= 16 \ \frac{c}{2} &= 16 - 6 \ \frac{c}{2} &= 10 \ c &= 10 \times 2 \ c &= 20 \end{aligned} $$ ## Solve equation d $$ \begin{aligned} 4x - 2 &= 10 \ 4x &= 10 + 2 \ 4x &= 12 \ x &= \frac{12}{4} \ x &= 3 \end{aligned} $$ ## Question a $a = -5$ ## Question b $b = 20$ ## Question c $c = 20$ ## Question d $x = 3$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Linear Equations" ] }

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