Solve for z 1/2-5/9z=-5/6

$\frac{1}{2} - \frac{5}{9} z = - \frac{5}{6}$

Simplify each term.

Combine $z$ and $\frac{5}{9}$ .

$\frac{1}{2} - \frac{z \cdot 5}{9} = - \frac{5}{6}$

Move $5$ to the left of $z$ .

$\frac{1}{2} - \frac{5 z}{9} = - \frac{5}{6}$

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$- \frac{5 z}{9} = - \frac{5}{6} - \frac{1}{2}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{5 z}{9} = - \frac{5}{6} - \frac{1}{2} \cdot \frac{3}{3}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

$- \frac{5 z}{9} = - \frac{5}{6} - \frac{3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$- \frac{5 z}{9} = - \frac{5}{6} - \frac{3}{6}$

Combine the numerators over the common denominator.

$- \frac{5 z}{9} = \frac{- 5 - 3}{6}$

Subtract $3$ from $- 5$ .

$- \frac{5 z}{9} = \frac{- 8}{6}$

Cancel the common factor of $- 8$ and $6$ .

Factor $2$ out of $- 8$ .

$- \frac{5 z}{9} = \frac{2 (- 4)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$- \frac{5 z}{9} = \frac{2 \cdot - 4}{2 \cdot 3}$

Cancel the common factor.

$- \frac{5 z}{9} = \frac{2 \cdot - 4}{2 \cdot 3}$

Rewrite the expression.

$- \frac{5 z}{9} = \frac{- 4}{3}$

Move the negative in front of the fraction.

$- \frac{5 z}{9} = - \frac{4}{3}$

Multiply both sides of the equation by $- \frac{9}{5}$ .

$- \frac{9}{5} (- \frac{5 z}{9}) = - \frac{9}{5} (- \frac{4}{3})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{9}{5} (- \frac{5 z}{9})$ .

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$\frac{- 9}{5} (- \frac{5 z}{9}) = - \frac{9}{5} (- \frac{4}{3})$

Move the leading negative in $- \frac{5 z}{9}$ into the numerator.

$\frac{- 9}{5} \cdot \frac{- 5 z}{9} = - \frac{9}{5} (- \frac{4}{3})$

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{5} \cdot \frac{- 5 z}{9} = - \frac{9}{5} (- \frac{4}{3})$

Cancel the common factor.

$\frac{9 \cdot - 1}{5} \cdot \frac{- 5 z}{9} = - \frac{9}{5} (- \frac{4}{3})$

Rewrite the expression.

$\frac{- 1}{5} (- 5 z) = - \frac{9}{5} (- \frac{4}{3})$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 z$ .

$\frac{- 1}{5} (5 (- z)) = - \frac{9}{5} (- \frac{4}{3})$

Cancel the common factor.

$\frac{- 1}{5} (5 (- z)) = - \frac{9}{5} (- \frac{4}{3})$

Rewrite the expression.

$- - z = - \frac{9}{5} (- \frac{4}{3})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{9}{5} (- \frac{4}{3})$

Multiply $z$ by $1$ .

$z = - \frac{9}{5} (- \frac{4}{3})$

Simplify the right side.

Simplify $- \frac{9}{5} (- \frac{4}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$z = \frac{- 9}{5} (- \frac{4}{3})$

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$z = \frac{- 9}{5} \cdot \frac{- 4}{3}$

Factor $3$ out of $- 9$ .

$z = \frac{3 (- 3)}{5} \cdot \frac{- 4}{3}$

Cancel the common factor.

$z = \frac{3 \cdot - 3}{5} \cdot \frac{- 4}{3}$

Rewrite the expression.

$z = \frac{- 3}{5} \cdot - 4$

Combine $\frac{- 3}{5}$ and $- 4$ .

$z = \frac{- 3 \cdot - 4}{5}$

Multiply $- 3$ by $- 4$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$z = 2.4$

Mixed Number Form:

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

Solve for z 1/2-5/9z=-5/6

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