Solve for x -9=2/3x-17

$- 9 = \frac{2}{3} x - 17$

Step 1

Rewrite the equation as $\frac{2}{3} x - 17 = - 9$ .

$\frac{2}{3} x - 17 = - 9$

Step 2

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} - 17 = - 9$

Step 3

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

Add $17$ to both sides of the equation.

$\frac{2 x}{3} = - 9 + 17$

Add $- 9$ and $17$ .

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

Step 4

Multiply both sides of the equation by $\frac{3}{2}$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{3}{2} \cdot 8$ .

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$x = \frac{3}{2} \cdot (2 (4))$

Cancel the common factor.

$x = \frac{3}{2} \cdot (2 \cdot 4)$

Rewrite the expression.

$x = 3 \cdot 4$

Multiply $3$ by $4$ .

$x = 12$