Solve for r 10/7-1/7r=-2/7r+25/7

$\frac{10}{7} - \frac{1}{7} r = - \frac{2}{7} r + \frac{25}{7}$

Step 1

Combine $r$ and $\frac{1}{7}$ .

$\frac{10}{7} - \frac{r}{7} = - \frac{2}{7} r + \frac{25}{7}$

Step 2

Simplify each term.

Combine $r$ and $\frac{2}{7}$ .

$\frac{10}{7} - \frac{r}{7} = - \frac{r \cdot 2}{7} + \frac{25}{7}$

Move $2$ to the left of $r$ .

$\frac{10}{7} - \frac{r}{7} = - \frac{2 r}{7} + \frac{25}{7}$

Step 3

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

Add $\frac{2 r}{7}$ to both sides of the equation.

$\frac{10}{7} - \frac{r}{7} + \frac{2 r}{7} = \frac{25}{7}$

Combine the numerators over the common denominator.

$\frac{10 - r + 2 r}{7} = \frac{25}{7}$

Add $- r$ and $2 r$ .

$\frac{10 + r}{7} = \frac{25}{7}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$10 + r = 25$

Step 5

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

Subtract $10$ from both sides of the equation.

$r = 25 - 10$

Subtract $10$ from $25$ .

$r = 15$