Solve for u -12u+3=8v+1

$- 12 u + 3 = 8 v + 1$

Step 1

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

Subtract $3$ from both sides of the equation.

$- 12 u = 8 v + 1 - 3$

Subtract $3$ from $1$ .

$- 12 u = 8 v - 2$

Step 2

Divide each term in $- 12 u = 8 v - 2$ by $- 12$ and simplify.

Divide each term in $- 12 u = 8 v - 2$ by $- 12$ .

$\frac{- 12 u}{- 12} = \frac{8 v}{- 12} + \frac{- 2}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 u}{- 12} = \frac{8 v}{- 12} + \frac{- 2}{- 12}$

Divide $u$ by $1$ .

$u = \frac{8 v}{- 12} + \frac{- 2}{- 12}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $8$ and $- 12$ .

Factor $4$ out of $8 v$ .

$u = \frac{4 (2 v)}{- 12} + \frac{- 2}{- 12}$

Cancel the common factors.

Factor $4$ out of $- 12$ .

$u = \frac{4 (2 v)}{4 (- 3)} + \frac{- 2}{- 12}$

Cancel the common factor.

$u = \frac{4 (2 v)}{4 \cdot - 3} + \frac{- 2}{- 12}$

Rewrite the expression.

$u = \frac{2 v}{- 3} + \frac{- 2}{- 12}$

Move the negative in front of the fraction.

$u = - \frac{2 v}{3} + \frac{- 2}{- 12}$

Cancel the common factor of $- 2$ and $- 12$ .

Factor $- 2$ out of $- 2$ .

$u = - \frac{2 v}{3} + \frac{- 2 (1)}{- 12}$

Cancel the common factors.

Factor $- 2$ out of $- 12$ .

$u = - \frac{2 v}{3} + \frac{- 2 \cdot 1}{- 2 \cdot 6}$

Cancel the common factor.

$u = - \frac{2 v}{3} + \frac{- 2 \cdot 1}{- 2 \cdot 6}$

Rewrite the expression.

$u = - \frac{2 v}{3} + \frac{1}{6}$