Solve for z 5/3z+1=3-2/3z

$\frac{5}{3} z + 1 = 3 - \frac{2}{3} z$

Combine $\frac{5}{3}$ and $z$ .

$\frac{5 z}{3} + 1 = 3 - \frac{2}{3} z$

Simplify each term.

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

$\frac{5 z}{3} + 1 = 3 - \frac{z \cdot 2}{3}$

Move $2$ to the left of $z$ .

$\frac{5 z}{3} + 1 = 3 - \frac{2 z}{3}$

Move all terms containing $z$ to the left side of the equation.

Add $\frac{2 z}{3}$ to both sides of the equation.

$\frac{5 z}{3} + 1 + \frac{2 z}{3} = 3$

Combine the numerators over the common denominator.

$1 + \frac{5 z + 2 z}{3} = 3$

Add $5 z$ and $2 z$ .

$1 + \frac{7 z}{3} = 3$

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

Subtract $1$ from both sides of the equation.

$\frac{7 z}{3} = 3 - 1$

Subtract $1$ from $3$ .

$\frac{7 z}{3} = 2$

Multiply both sides of the equation by $\frac{3}{7}$ .

$\frac{3}{7} \cdot \frac{7 z}{3} = \frac{3}{7} \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{7} \cdot \frac{7 z}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{7} \cdot \frac{7 z}{3} = \frac{3}{7} \cdot 2$

Rewrite the expression.

$\frac{1}{7} (7 z) = \frac{3}{7} \cdot 2$

Cancel the common factor of $7$ .

Factor $7$ out of $7 z$ .

$\frac{1}{7} (7 (z)) = \frac{3}{7} \cdot 2$

Cancel the common factor.

$\frac{1}{7} (7 z) = \frac{3}{7} \cdot 2$

Rewrite the expression.

$z = \frac{3}{7} \cdot 2$

Simplify the right side.

Multiply $\frac{3}{7} \cdot 2$ .

Combine $\frac{3}{7}$ and $2$ .

$z = \frac{3 \cdot 2}{7}$

Multiply $3$ by $2$ .

$z = \frac{6}{7}$

The result can be shown in multiple forms.

Exact Form:

$z = \frac{6}{7}$

Decimal Form:

$z = 0.\overline{857142}$

Solve for z 5/3z+1=3-2/3z

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