Solve for g 1/6g+4/9=g-1/9

$\frac{1}{6} g + \frac{4}{9} = g - \frac{1}{9}$

Step 1

Combine $\frac{1}{6}$ and $g$ .

$\frac{g}{6} + \frac{4}{9} = g - \frac{1}{9}$

Step 2

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

Subtract $g$ from both sides of the equation.

$\frac{g}{6} + \frac{4}{9} - g = - \frac{1}{9}$

To write $- g$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{g}{6} - g \cdot \frac{6}{6} + \frac{4}{9} = - \frac{1}{9}$

Combine $- g$ and $\frac{6}{6}$ .

$\frac{g}{6} + \frac{- g \cdot 6}{6} + \frac{4}{9} = - \frac{1}{9}$

Combine the numerators over the common denominator.

$\frac{g - g \cdot 6}{6} + \frac{4}{9} = - \frac{1}{9}$

Simplify each term.

Simplify the numerator.

Factor $g$ out of $g - g \cdot 6$ .

Raise $g$ to the power of $1$ .

$\frac{g^{1} - g \cdot 6}{6} + \frac{4}{9} = - \frac{1}{9}$

Factor $g$ out of $g^{1}$ .

$\frac{g \cdot 1 - g \cdot 6}{6} + \frac{4}{9} = - \frac{1}{9}$

Factor $g$ out of $- g \cdot 6$ .

$\frac{g \cdot 1 + g (- 1 \cdot 6)}{6} + \frac{4}{9} = - \frac{1}{9}$

Factor $g$ out of $g \cdot 1 + g (- 1 \cdot 6)$ .

$\frac{g (1 - 1 \cdot 6)}{6} + \frac{4}{9} = - \frac{1}{9}$

Multiply $- 1$ by $6$ .

$\frac{g (1 - 6)}{6} + \frac{4}{9} = - \frac{1}{9}$

Subtract $6$ from $1$ .

$\frac{g \cdot - 5}{6} + \frac{4}{9} = - \frac{1}{9}$

Move $- 5$ to the left of $g$ .

$\frac{- 5 \cdot g}{6} + \frac{4}{9} = - \frac{1}{9}$

Move the negative in front of the fraction.

$- \frac{5 g}{6} + \frac{4}{9} = - \frac{1}{9}$

Step 3

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

Subtract $\frac{4}{9}$ from both sides of the equation.

$- \frac{5 g}{6} = - \frac{1}{9} - \frac{4}{9}$

Combine the numerators over the common denominator.

$- \frac{5 g}{6} = \frac{- 1 - 4}{9}$

Subtract $4$ from $- 1$ .

$- \frac{5 g}{6} = \frac{- 5}{9}$

Move the negative in front of the fraction.

$- \frac{5 g}{6} = - \frac{5}{9}$

Step 4

Multiply both sides of the equation by $- \frac{6}{5}$ .

$- \frac{6}{5} (- \frac{5 g}{6}) = - \frac{6}{5} (- \frac{5}{9})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{5} (- \frac{5 g}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{- 6}{5} (- \frac{5 g}{6}) = - \frac{6}{5} (- \frac{5}{9})$

Move the leading negative in $- \frac{5 g}{6}$ into the numerator.

$\frac{- 6}{5} \cdot \frac{- 5 g}{6} = - \frac{6}{5} (- \frac{5}{9})$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{5} \cdot \frac{- 5 g}{6} = - \frac{6}{5} (- \frac{5}{9})$

Cancel the common factor.

$\frac{6 \cdot - 1}{5} \cdot \frac{- 5 g}{6} = - \frac{6}{5} (- \frac{5}{9})$

Rewrite the expression.

$\frac{- 1}{5} (- 5 g) = - \frac{6}{5} (- \frac{5}{9})$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 g$ .

$\frac{- 1}{5} (5 (- g)) = - \frac{6}{5} (- \frac{5}{9})$

Cancel the common factor.

$\frac{- 1}{5} (5 (- g)) = - \frac{6}{5} (- \frac{5}{9})$

Rewrite the expression.

$- - g = - \frac{6}{5} (- \frac{5}{9})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 g = - \frac{6}{5} (- \frac{5}{9})$

Multiply $g$ by $1$ .

$g = - \frac{6}{5} (- \frac{5}{9})$

Simplify the right side.

Simplify $- \frac{6}{5} (- \frac{5}{9})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$g = \frac{- 6}{5} (- \frac{5}{9})$

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

$g = \frac{- 6}{5} \cdot \frac{- 5}{9}$

Factor $3$ out of $- 6$ .

$g = \frac{3 (- 2)}{5} \cdot \frac{- 5}{9}$

Factor $3$ out of $9$ .

$g = \frac{3 \cdot - 2}{5} \cdot \frac{- 5}{3 \cdot 3}$

Cancel the common factor.

$g = \frac{3 \cdot - 2}{5} \cdot \frac{- 5}{3 \cdot 3}$

Rewrite the expression.

$g = \frac{- 2}{5} \cdot \frac{- 5}{3}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$g = \frac{- 2}{5} \cdot \frac{5 (- 1)}{3}$

Cancel the common factor.

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

Rewrite the expression.

$g = - 2 (\frac{- 1}{3})$

Combine $- 2$ and $\frac{- 1}{3}$ .

$g = \frac{- 2 \cdot - 1}{3}$

Multiply $- 2$ by $- 1$ .

$g = \frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$g = \frac{2}{3}$

Decimal Form:

$g = 0.\overline{6}$

Solve for g 1/6g+4/9=g-1/9

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