Solve for x x+10/9=8/9x

$x + \frac{10}{9} = \frac{8}{9} x$

Step 1

Simplify $\frac{8}{9} x$ .

Rewrite.

$x + \frac{10}{9} = 0 + 0 + \frac{8}{9} x$

Simplify by adding zeros.

$x + \frac{10}{9} = \frac{8}{9} x$

Combine $\frac{8}{9}$ and $x$ .

$x + \frac{10}{9} = \frac{8 x}{9}$

Step 2

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

Subtract $\frac{8 x}{9}$ from both sides of the equation.

$x + \frac{10}{9} - \frac{8 x}{9} = 0$

To write $x$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$x \cdot \frac{9}{9} - \frac{8 x}{9} + \frac{10}{9} = 0$

Combine $x$ and $\frac{9}{9}$ .

$\frac{x \cdot 9}{9} - \frac{8 x}{9} + \frac{10}{9} = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 9 - 8 x}{9} + \frac{10}{9} = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 9 - 8 x + 10}{9} = 0$

Move $9$ to the left of $x$ .

$\frac{9 x - 8 x + 10}{9} = 0$

Subtract $8 x$ from $9 x$ .

$\frac{x + 10}{9} = 0$

Step 3

Set the numerator equal to zero.

$x + 10 = 0$

Step 4

Subtract $10$ from both sides of the equation.

$x = - 10$