Solve for v u-5=-4(v-1)

$u - 5 = - 4 (v - 1)$

Rewrite the equation as $- 4 (v - 1) = u - 5$ .

$- 4 (v - 1) = u - 5$

Divide each term in $- 4 (v - 1) = u - 5$ by $- 4$ and simplify.

Divide each term in $- 4 (v - 1) = u - 5$ by $- 4$ .

$\frac{- 4 (v - 1)}{- 4} = \frac{u}{- 4} + \frac{- 5}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 (v - 1)}{- 4} = \frac{u}{- 4} + \frac{- 5}{- 4}$

Divide $v - 1$ by $1$ .

$v - 1 = \frac{u}{- 4} + \frac{- 5}{- 4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$v - 1 = - \frac{u}{4} + \frac{- 5}{- 4}$

Dividing two negative values results in a positive value.

$v - 1 = - \frac{u}{4} + \frac{5}{4}$

Move all terms not containing $v$ to the right side of the equation.

Add $1$ to both sides of the equation.

$v = - \frac{u}{4} + \frac{5}{4} + 1$

Write $1$ as a fraction with a common denominator.

$v = - \frac{u}{4} + \frac{5}{4} + \frac{4}{4}$

Combine the numerators over the common denominator.

$v = - \frac{u}{4} + \frac{5 + 4}{4}$

Add $5$ and $4$ .

$v = - \frac{u}{4} + \frac{9}{4}$