Solve for z z-3/4=-1/3

$z - \frac{3}{4} = - \frac{1}{3}$

Add $\frac{3}{4}$ to both sides of the equation.

$z = - \frac{1}{3} + \frac{3}{4}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$z = - \frac{1}{3} \cdot \frac{4}{4} + \frac{3}{4}$

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

$z = - \frac{1}{3} \cdot \frac{4}{4} + \frac{3}{4} \cdot \frac{3}{3}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$z = - \frac{4}{3 \cdot 4} + \frac{3}{4} \cdot \frac{3}{3}$

Multiply $3$ by $4$ .

$z = - \frac{4}{12} + \frac{3}{4} \cdot \frac{3}{3}$

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$z = - \frac{4}{12} + \frac{3 \cdot 3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$z = - \frac{4}{12} + \frac{3 \cdot 3}{12}$

Combine the numerators over the common denominator.

$z = \frac{- 4 + 3 \cdot 3}{12}$

Simplify the numerator.

Multiply $3$ by $3$ .

$z = \frac{- 4 + 9}{12}$

Add $- 4$ and $9$ .

$z = \frac{5}{12}$

The result can be shown in multiple forms.

Exact Form:

$z = \frac{5}{12}$

Decimal Form:

$z = 0.41\overline{6}$