Solve for z 2/3z+z=2/3

$\frac{2}{3} z + z = \frac{2}{3}$

Step 1

Simplify $\frac{2}{3} z + z$ .

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

$\frac{2 z}{3} + z = \frac{2}{3}$

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

$\frac{2 z}{3} + z \cdot \frac{3}{3} = \frac{2}{3}$

Simplify terms.

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

$\frac{2 z}{3} + \frac{z \cdot 3}{3} = \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{2 z + z \cdot 3}{3} = \frac{2}{3}$

Simplify the numerator.

Move $3$ to the left of $z$ .

$\frac{2 z + 3 \cdot z}{3} = \frac{2}{3}$

Add $2 z$ and $3 z$ .

$\frac{5 z}{3} = \frac{2}{3}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 z = 2$

Step 3

Divide each term in $5 z = 2$ by $5$ and simplify.

Divide each term in $5 z = 2$ by $5$ .

$\frac{5 z}{5} = \frac{2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 z}{5} = \frac{2}{5}$

Divide $z$ by $1$ .

$z = \frac{2}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{2}{5}$

Decimal Form:

$z = 0.4$