Question

solve for (v).

-3(-4v+3)-4v=2(v-2)-1

simplify your answer as much as possible.

(v = )

Explanation:

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<reasoning>

Apply the distributive property

Using the Distributive Property knowledge point
\[

$$\begin{aligned} -3(-4v + 3) - 4v &= 2(v - 2) - 1 \\ 12v - 9 - 4v &= 2v - 4 - 1 \end{aligned}$$

\]

Combine like terms on both sides

Using the Linear Equation Solutions knowledge point
\[

$$\begin{aligned} (12v - 4v) - 9 &= 2v - (4 + 1) \\ 8v - 9 &= 2v - 5 \end{aligned}$$

\]

Isolate the variable terms

Using the Linear Equation Solutions knowledge point
\[

$$\begin{aligned} 8v - 2v &= -5 + 9 \\ 6v &= 4 \end{aligned}$$

\]

Solve for v and simplify

Using the Linear Equation Solutions knowledge point
\[

$$\begin{aligned} v &= \frac{4}{6} \\ v &= \frac{2}{3} \end{aligned}$$

\]
</reasoning>

<answer>
Solve for \(v\).

\[-3(-4v+3)-4v=2(v-2)-1\]

Simplify your answer as much as possible.

\(v =\) <blank>\(\frac{2}{3}\)</blank>
</answer>

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Answer:

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<reasoning>

Apply the distributive property

Using the Distributive Property knowledge point
\[

$$\begin{aligned} -3(-4v + 3) - 4v &= 2(v - 2) - 1 \\ 12v - 9 - 4v &= 2v - 4 - 1 \end{aligned}$$

\]

Combine like terms on both sides

Using the Linear Equation Solutions knowledge point
\[

$$\begin{aligned} (12v - 4v) - 9 &= 2v - (4 + 1) \\ 8v - 9 &= 2v - 5 \end{aligned}$$

\]

Isolate the variable terms

Using the Linear Equation Solutions knowledge point
\[

$$\begin{aligned} 8v - 2v &= -5 + 9 \\ 6v &= 4 \end{aligned}$$

\]

Solve for v and simplify

Using the Linear Equation Solutions knowledge point
\[

$$\begin{aligned} v &= \frac{4}{6} \\ v &= \frac{2}{3} \end{aligned}$$

\]
</reasoning>

<answer>
Solve for \(v\).

\[-3(-4v+3)-4v=2(v-2)-1\]

Simplify your answer as much as possible.

\(v =\) <blank>\(\frac{2}{3}\)</blank>
</answer>

<post_analysis>
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"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equation Solutions"
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