Question

solve for (v).

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

simplify your answer as much as possible.

Explanation:

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 \(2\):

$$ v = -\frac{9}{8} $$

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>