Solve for x 2/3(1+x)=a

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

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

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

Simplify both sides of the equation.

Simplify the left side.

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

Apply the distributive property.

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

Multiply $\frac{2}{3}$ by $1$ .

$\frac{3}{2} (\frac{2}{3} + \frac{2}{3} x) = \frac{3}{2} a$

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

$\frac{3}{2} (\frac{2}{3} + \frac{2 x}{3}) = \frac{3}{2} a$

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2}{3} + \frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} a$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2}{3} + \frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} a$

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$1 + x = \frac{3}{2} a$

Simplify the right side.

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

$1 + x = \frac{3 a}{2}$

Subtract $1$ from both sides of the equation.

$x = \frac{3 a}{2} - 1$