Question

solve for (v).

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

simplify your answer as much as possible.

Explanation:

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<reasoning>

Apply the distributive property

Using the Distributive Property, we expand the terms inside the parentheses on both sides of the equation.
On the left side:
\[
-4(-4v - 1) = 16v + 4
\]
On the right side:
\[
4(v - 2) = 4v - 8
\]
Substitute these back into the equation:
\[
4v + 6 + 16v + 4 = 4v - 8
\]

Combine like terms

Combine the variable terms and constant terms on the left side of the equation.
\[
(4v + 16v) + (6 + 4) = 4v - 8
\]
\[
20v + 10 = 4v - 8
\]

Isolate the variable terms

Subtract \(4v\) from both sides to gather all terms with \(v\) on the left side.
Using the Linear Equation Solutions concept:
\[
20v - 4v + 10 = -8
\]
\[
16v + 10 = -8
\]

Isolate the constant terms

Subtract \(10\) from both sides of the equation to isolate the term with \(v\).
\[
16v = -8 - 10
\]
\[
16v = -18
\]

Solve for v and simplify

Divide both sides by \(16\) and simplify the resulting fraction to its lowest terms.
\[
v = -\frac{18}{16}
\]
Divide the numerator and denominator by their greatest common divisor, which is \(2\):
\[
v = -\frac{9}{8}
\]
</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, we expand the terms inside the parentheses on both sides of the equation.
On the left side:
\[
-4(-4v - 1) = 16v + 4
\]
On the right side:
\[
4(v - 2) = 4v - 8
\]
Substitute these back into the equation:
\[
4v + 6 + 16v + 4 = 4v - 8
\]

Combine like terms

Combine the variable terms and constant terms on the left side of the equation.
\[
(4v + 16v) + (6 + 4) = 4v - 8
\]
\[
20v + 10 = 4v - 8
\]

Isolate the variable terms

Subtract \(4v\) from both sides to gather all terms with \(v\) on the left side.
Using the Linear Equation Solutions concept:
\[
20v - 4v + 10 = -8
\]
\[
16v + 10 = -8
\]

Isolate the constant terms

Subtract \(10\) from both sides of the equation to isolate the term with \(v\).
\[
16v = -8 - 10
\]
\[
16v = -18
\]

Solve for v and simplify

Divide both sides by \(16\) and simplify the resulting fraction to its lowest terms.
\[
v = -\frac{18}{16}
\]
Divide the numerator and denominator by their greatest common divisor, which is \(2\):
\[
v = -\frac{9}{8}
\]
</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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