Question

solve for (v).

(4v + 6 - 4(-4v - 1) = 4(v - 2))

simplify your answer as much as possible.

(v = )

Explanation:

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<reasoning>

Apply the distributive property

Using the Distributive Property knowledge point
\[

$$\begin{aligned} &4v + 6 - 4(-4v - 1) = 4(v - 2) \\ &4v + 6 + 16v + 4 = 4v - 8 \end{aligned}$$

\]

Combine like terms on the left side

Using the Order of Operations knowledge point
\[

$$\begin{aligned} &(4v + 16v) + (6 + 4) = 4v - 8 \\ &20v + 10 = 4v - 8 \end{aligned}$$

\]

Isolate the variable terms

Using the Linear Equation Solutions knowledge point
\[

$$\begin{aligned} &20v - 4v = -8 - 10 \\ &16v = -18 \end{aligned}$$

\]

Solve for v

Using the Solving for a Variable knowledge point
\[

$$\begin{aligned} &v = \frac{-18}{16} \\ &v = -\frac{9}{8} \end{aligned}$$

\]
</reasoning>

<answer>
Solve for \(v\).

\(4v+6-4(-4v-1)=4(v-2)\)

Simplify your answer as much as possible.

\(v =\) <blank>\(-\frac{9}{8}\)</blank>
</answer>

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Answer:

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<reasoning>

Apply the distributive property

Using the Distributive Property knowledge point
\[

$$\begin{aligned} &4v + 6 - 4(-4v - 1) = 4(v - 2) \\ &4v + 6 + 16v + 4 = 4v - 8 \end{aligned}$$

\]

Combine like terms on the left side

Using the Order of Operations knowledge point
\[

$$\begin{aligned} &(4v + 16v) + (6 + 4) = 4v - 8 \\ &20v + 10 = 4v - 8 \end{aligned}$$

\]

Isolate the variable terms

Using the Linear Equation Solutions knowledge point
\[

$$\begin{aligned} &20v - 4v = -8 - 10 \\ &16v = -18 \end{aligned}$$

\]

Solve for v

Using the Solving for a Variable knowledge point
\[

$$\begin{aligned} &v = \frac{-18}{16} \\ &v = -\frac{9}{8} \end{aligned}$$

\]
</reasoning>

<answer>
Solve for \(v\).

\(4v+6-4(-4v-1)=4(v-2)\)

Simplify your answer as much as possible.

\(v =\) <blank>\(-\frac{9}{8}\)</blank>
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equation Solutions"
]
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