Solve 2/3(1+x)=a

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

Solve for a

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

Solution Steps

Use the distributive property to multiply \frac{2}{3} by 1+x.

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

Swap sides so that all variable terms are on the left hand side.

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 1+x.

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

Subtract \frac{2}{3} from both sides.

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

Divide both sides of the equation by \frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

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

Dividing by \frac{2}{3} undoes the multiplication by \frac{2}{3}.

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

Divide a-\frac{2}{3} by \frac{2}{3} by multiplying a-\frac{2}{3} by the reciprocal of \frac{2}{3}.

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