Solve for x 2/3x-2=7

$\frac{2}{3} x - 2 = 7$

Step 1

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

$\frac{2 x}{3} - 2 = 7$

Step 2

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

Add $2$ to both sides of the equation.

$\frac{2 x}{3} = 7 + 2$

Add $7$ and $2$ .

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

Step 3

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

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 9$

Step 4

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.

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 9$

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 9$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{3}{2} \cdot 9$

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 9$

Rewrite the expression.

$x = \frac{3}{2} \cdot 9$

Simplify the right side.

Multiply $\frac{3}{2} \cdot 9$ .

Combine $\frac{3}{2}$ and $9$ .

$x = \frac{3 \cdot 9}{2}$

Multiply $3$ by $9$ .

$x = \frac{27}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{27}{2}$

Decimal Form:

$x = 13.5$

Mixed Number Form:

$x = 13 \frac{1}{2}$