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

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

Step 1

Rewrite the equation as $- \frac{1}{6} + \frac{1}{9} z = - \frac{1}{2}$ .

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

Step 2

Combine $\frac{1}{9}$ and $z$ .

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

Step 3

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

Add $\frac{1}{6}$ to both sides of the equation.

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

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

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

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

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

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

Multiply $2$ by $3$ .

$\frac{z}{9} = - \frac{3}{6} + \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{z}{9} = \frac{- 3 + 1}{6}$

Add $- 3$ and $1$ .

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

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{z}{9} = \frac{- 1}{3}$

Move the negative in front of the fraction.

$\frac{z}{9} = - \frac{1}{3}$

Step 4

Multiply both sides of the equation by $9$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $9 (- \frac{1}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$z = 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$z = - 3$

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

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