Solve for x 8(x-1)+2/3=2/3

$8 (x - 1) + \frac{2}{3} = \frac{2}{3}$

Step 1

Simplify $8 (x - 1) + \frac{2}{3}$ .

Simplify each term.

Apply the distributive property.

$8 x + 8 \cdot - 1 + \frac{2}{3} = \frac{2}{3}$

Multiply $8$ by $- 1$ .

$8 x - 8 + \frac{2}{3} = \frac{2}{3}$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$8 x - 8 \cdot \frac{3}{3} + \frac{2}{3} = \frac{2}{3}$

Combine $- 8$ and $\frac{3}{3}$ .

$8 x + \frac{- 8 \cdot 3}{3} + \frac{2}{3} = \frac{2}{3}$

Combine the numerators over the common denominator.

$8 x + \frac{- 8 \cdot 3 + 2}{3} = \frac{2}{3}$

Simplify the numerator.

Multiply $- 8$ by $3$ .

$8 x + \frac{- 24 + 2}{3} = \frac{2}{3}$

Add $- 24$ and $2$ .

$8 x + \frac{- 22}{3} = \frac{2}{3}$

Move the negative in front of the fraction.

$8 x - \frac{22}{3} = \frac{2}{3}$

Step 2

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

Add $\frac{22}{3}$ to both sides of the equation.

$8 x = \frac{2}{3} + \frac{22}{3}$

Combine the numerators over the common denominator.

$8 x = \frac{2 + 22}{3}$

Add $2$ and $22$ .

$8 x = \frac{24}{3}$

Divide $24$ by $3$ .

$8 x = 8$

Step 3

Divide each term in $8 x = 8$ by $8$ and simplify.

Divide each term in $8 x = 8$ by $8$ .

$\frac{8 x}{8} = \frac{8}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{8}{8}$

Divide $x$ by $1$ .

$x = \frac{8}{8}$

Simplify the right side.

Divide $8$ by $8$ .

$x = 1$