Solve for u 5/6u+2-u=1/6u

$\frac{5}{6} u + 2 - u = \frac{1}{6} u$

Step 1

Simplify $\frac{5}{6} u + 2 - u$ .

Combine $\frac{5}{6}$ and $u$ .

$\frac{5 u}{6} + 2 - u = \frac{1}{6} u$

To write $- u$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 u}{6} - u \cdot \frac{6}{6} + 2 = \frac{1}{6} u$

Simplify terms.

Combine $- u$ and $\frac{6}{6}$ .

$\frac{5 u}{6} + \frac{- u \cdot 6}{6} + 2 = \frac{1}{6} u$

Combine the numerators over the common denominator.

$\frac{5 u - u \cdot 6}{6} + 2 = \frac{1}{6} u$

Simplify each term.

Simplify the numerator.

Factor $u$ out of $5 u - u \cdot 6$ .

Factor $u$ out of $5 u$ .

$\frac{u \cdot 5 - u \cdot 6}{6} + 2 = \frac{1}{6} u$

Factor $u$ out of $- u \cdot 6$ .

$\frac{u \cdot 5 + u (- 1 \cdot 6)}{6} + 2 = \frac{1}{6} u$

Factor $u$ out of $u \cdot 5 + u (- 1 \cdot 6)$ .

$\frac{u (5 - 1 \cdot 6)}{6} + 2 = \frac{1}{6} u$

Multiply $- 1$ by $6$ .

$\frac{u (5 - 6)}{6} + 2 = \frac{1}{6} u$

Subtract $6$ from $5$ .

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

Move $- 1$ to the left of $u$ .

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

Move the negative in front of the fraction.

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

Step 2

Combine $\frac{1}{6}$ and $u$ .

$- \frac{u}{6} + 2 = \frac{u}{6}$

Step 3

Move all terms containing $u$ to the left side of the equation.

Subtract $\frac{u}{6}$ from both sides of the equation.

$- \frac{u}{6} + 2 - \frac{u}{6} = 0$

Combine the numerators over the common denominator.

$2 + \frac{- u - u}{6} = 0$

Subtract $u$ from $- u$ .

$2 + \frac{- 2 u}{6} = 0$

Simplify each term.

Cancel the common factor of $- 2$ and $6$ .

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

$2 + \frac{2 (- u)}{6} = 0$

Cancel the common factors.

Factor $2$ out of $6$ .

$2 + \frac{2 (- u)}{2 (3)} = 0$

Cancel the common factor.

$2 + \frac{2 (- u)}{2 \cdot 3} = 0$

Rewrite the expression.

$2 + \frac{- u}{3} = 0$

Move the negative in front of the fraction.

$2 - \frac{u}{3} = 0$

Step 4

Subtract $2$ from both sides of the equation.

$- \frac{u}{3} = - 2$

Step 5

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{u}{3}) = - 3 \cdot - 2$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{u}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{u}{3}$ into the numerator.

$- 3 \frac{- u}{3} = - 3 \cdot - 2$

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- u}{3} = - 3 \cdot - 2$

Cancel the common factor.

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

Rewrite the expression.

$- - u = - 3 \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 u = - 3 \cdot - 2$

Multiply $u$ by $1$ .

$u = - 3 \cdot - 2$

Simplify the right side.

Multiply $- 3$ by $- 2$ .

$u = 6$

Solve for u 5/6u+2-u=1/6u

Related Questions

Support LCMGCF.com by disabling your adblocker.