2 if $\frac{6 + a}{12} = \frac{2}{3}$, then $a = \underline{\quad\quad}$.

3 solve the equation: $12 - 4(x - 1) = 5(x - 3)$.

$x = \underline{\quad\quad}$.

Question

2 if $\frac{6 + a}{12} = \frac{2}{3}$, then $a = \underline{\quad\quad}$.

3 solve the equation: $12 - 4(x - 1) = 5(x - 3)$.

$x = \underline{\quad\quad}$.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Linear Equations", "Distributive Property" ], "new_concepts": [], "current_concepts": [ "Solving Linear Equations", "Distributive Property" ] } ## Solve for a in the first equation $$ \begin{aligned} \frac{6 + a}{12} &= \frac{2}{3} \ 6 + a &= 12 \cdot \frac{2}{3} \ 6 + a &= 8 \ a &= 2 \end{aligned} $$ ## Solve for x in the second equation $$ \begin{aligned} 12 - 4(x - 1) &= 5(x - 3) \ 12 - 4x + 4 &= 5x - 15 \ 16 - 4x &= 5x - 15 \ 16 + 15 &= 5x + 4x \ 31 &= 9x \ x &= \frac{31}{9} \end{aligned} $$ ## Question 2 If $\frac{6 + a}{12} = \frac{2}{3}$, then $a =$ 2. ## Question 3 Solve the equation: $12 - 4(x - 1) = 5(x - 3)$ $x =$ $\frac{31}{9}$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Solve for a in the first equation

Solve for x in the second equation

Answer:

Question 2

Question 3