Solve for x 2/9x-4=2/3

$\frac{2}{9} x - 4 = \frac{2}{3}$

Step 1

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

$\frac{2 x}{9} - 4 = \frac{2}{3}$

Step 2

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

Add $4$ to both sides of the equation.

$\frac{2 x}{9} = \frac{2}{3} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{9} = \frac{2}{3} + 4 \cdot \frac{3}{3}$

Combine $4$ and $\frac{3}{3}$ .

$\frac{2 x}{9} = \frac{2}{3} + \frac{4 \cdot 3}{3}$

Combine the numerators over the common denominator.

$\frac{2 x}{9} = \frac{2 + 4 \cdot 3}{3}$

Simplify the numerator.

Multiply $4$ by $3$ .

$\frac{2 x}{9} = \frac{2 + 12}{3}$

Add $2$ and $12$ .

$\frac{2 x}{9} = \frac{14}{3}$

Step 3

Multiply both sides of the equation by $\frac{9}{2}$ .

$\frac{9}{2} \cdot \frac{2 x}{9} = \frac{9}{2} \cdot \frac{14}{3}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{9}{2} \cdot \frac{2 x}{9}$ .

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 x}{9} = \frac{9}{2} \cdot \frac{14}{3}$

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{9}{2} \cdot \frac{14}{3}$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{9}{2} \cdot \frac{14}{3}$

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{9}{2} \cdot \frac{14}{3}$

Rewrite the expression.

$x = \frac{9}{2} \cdot \frac{14}{3}$

Simplify the right side.

Simplify $\frac{9}{2} \cdot \frac{14}{3}$ .

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$x = \frac{3 (3)}{2} \cdot \frac{14}{3}$

Cancel the common factor.

$x = \frac{3 \cdot 3}{2} \cdot \frac{14}{3}$

Rewrite the expression.

$x = \frac{3}{2} \cdot 14$

Cancel the common factor of $2$ .

Factor $2$ out of $14$ .

$x = \frac{3}{2} \cdot (2 (7))$

Cancel the common factor.

$x = \frac{3}{2} \cdot (2 \cdot 7)$

Rewrite the expression.

$x = 3 \cdot 7$

Multiply $3$ by $7$ .

$x = 21$

Solve for x 2/9x-4=2/3

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