Solve for u -7/5u-1/5=5u-5/2

$- \frac{7}{5} u - \frac{1}{5} = 5 u - \frac{5}{2}$

Step 1

Simplify each term.

Combine $u$ and $\frac{7}{5}$ .

$- \frac{u \cdot 7}{5} - \frac{1}{5} = 5 u - \frac{5}{2}$

Move $7$ to the left of $u$ .

$- \frac{7 u}{5} - \frac{1}{5} = 5 u - \frac{5}{2}$

Step 2

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

Subtract $5 u$ from both sides of the equation.

$- \frac{7 u}{5} - \frac{1}{5} - 5 u = - \frac{5}{2}$

To write $- 5 u$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{7 u}{5} - 5 u \cdot \frac{5}{5} - \frac{1}{5} = - \frac{5}{2}$

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

$- \frac{7 u}{5} + \frac{- 5 u \cdot 5}{5} - \frac{1}{5} = - \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{- 7 u - 5 u \cdot 5}{5} - \frac{1}{5} = - \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{- 7 u - 5 u \cdot 5 - 1}{5} = - \frac{5}{2}$

Multiply $5$ by $- 5$ .

$\frac{- 7 u - 25 u - 1}{5} = - \frac{5}{2}$

Subtract $25 u$ from $- 7 u$ .

$\frac{- 32 u - 1}{5} = - \frac{5}{2}$

Factor $- 1$ out of $- 32 u$ .

$\frac{- (32 u) - 1}{5} = - \frac{5}{2}$

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- (32 u) - 1 (1)}{5} = - \frac{5}{2}$

Factor $- 1$ out of $- (32 u) - 1 (1)$ .

$\frac{- (32 u + 1)}{5} = - \frac{5}{2}$

Rewrite $- (32 u + 1)$ as $- 1 (32 u + 1)$ .

$\frac{- 1 (32 u + 1)}{5} = - \frac{5}{2}$

Move the negative in front of the fraction.

$- \frac{32 u + 1}{5} = - \frac{5}{2}$

Step 3

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{32 u + 1}{5}) = - 5 (- \frac{5}{2})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 5 (- \frac{32 u + 1}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{32 u + 1}{5}$ into the numerator.

$- 5 \frac{- (32 u + 1)}{5} = - 5 (- \frac{5}{2})$

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- (32 u + 1)}{5} = - 5 (- \frac{5}{2})$

Cancel the common factor.

$5 \cdot - 1 \frac{- (32 u + 1)}{5} = - 5 (- \frac{5}{2})$

Rewrite the expression.

$- - (32 u + 1) = - 5 (- \frac{5}{2})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (32 u + 1) = - 5 (- \frac{5}{2})$

Multiply $32 u + 1$ by $1$ .

$32 u + 1 = - 5 (- \frac{5}{2})$

Simplify the right side.

Multiply $- 5 (- \frac{5}{2})$ .

Multiply $- 1$ by $- 5$ .

$32 u + 1 = 5 (\frac{5}{2})$

Combine $5$ and $\frac{5}{2}$ .

$32 u + 1 = \frac{5 \cdot 5}{2}$

Multiply $5$ by $5$ .

$32 u + 1 = \frac{25}{2}$

Step 5

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

Subtract $1$ from both sides of the equation.

$32 u = \frac{25}{2} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$32 u = \frac{25}{2} - 1 \cdot \frac{2}{2}$

Combine $- 1$ and $\frac{2}{2}$ .

$32 u = \frac{25}{2} + \frac{- 1 \cdot 2}{2}$

Combine the numerators over the common denominator.

$32 u = \frac{25 - 1 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$32 u = \frac{25 - 2}{2}$

Subtract $2$ from $25$ .

$32 u = \frac{23}{2}$

Step 6

Divide each term in $32 u = \frac{23}{2}$ by $32$ and simplify.

Divide each term in $32 u = \frac{23}{2}$ by $32$ .

$\frac{32 u}{32} = \frac{\frac{23}{2}}{32}$

Simplify the left side.

Cancel the common factor of $32$ .

Cancel the common factor.

$\frac{32 u}{32} = \frac{\frac{23}{2}}{32}$

Divide $u$ by $1$ .

$u = \frac{\frac{23}{2}}{32}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$u = \frac{23}{2} \cdot \frac{1}{32}$

Multiply $\frac{23}{2} \cdot \frac{1}{32}$ .

Multiply $\frac{23}{2}$ by $\frac{1}{32}$ .

$u = \frac{23}{2 \cdot 32}$

Multiply $2$ by $32$ .

$u = \frac{23}{64}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$u = \frac{23}{64}$

Decimal Form:

$u = 0.359375$

Solve for u -7/5u-1/5=5u-5/2

Related Questions