Solve for g -1/2g+1/4-2g=-2-5/8g+1

$- \frac{1}{2} g + \frac{1}{4} - 2 g = - 2 - \frac{5}{8} g + 1$

Simplify $- \frac{1}{2} g + \frac{1}{4} - 2 g$ .

Combine $g$ and $\frac{1}{2}$ .

$- \frac{g}{2} + \frac{1}{4} - 2 g = - 2 - \frac{5}{8} g + 1$

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

$- \frac{g}{2} - 2 g \cdot \frac{2}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Simplify terms.

Combine $- 2 g$ and $\frac{2}{2}$ .

$- \frac{g}{2} + \frac{- 2 g \cdot 2}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Combine the numerators over the common denominator.

$\frac{- g - 2 g \cdot 2}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Simplify each term.

Simplify the numerator.

Factor $g$ out of $- g - 2 g \cdot 2$ .

Factor $g$ out of $- g$ .

$\frac{g \cdot - 1 - 2 g \cdot 2}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Factor $g$ out of $- 2 g \cdot 2$ .

$\frac{g \cdot - 1 + g (- 2 \cdot 2)}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Factor $g$ out of $g \cdot - 1 + g (- 2 \cdot 2)$ .

$\frac{g (- 1 - 2 \cdot 2)}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Multiply $- 2$ by $2$ .

$\frac{g (- 1 - 4)}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Subtract $4$ from $- 1$ .

$\frac{g \cdot - 5}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

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

$\frac{- 5 \cdot g}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Move the negative in front of the fraction.

$- \frac{5 g}{2} + \frac{1}{4} = - 2 - \frac{5}{8} g + 1$

Simplify $- 2 - \frac{5}{8} g + 1$ .

Simplify each term.

Combine $g$ and $\frac{5}{8}$ .

$- \frac{5 g}{2} + \frac{1}{4} = - 2 - \frac{g \cdot 5}{8} + 1$

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

$- \frac{5 g}{2} + \frac{1}{4} = - 2 - \frac{5 g}{8} + 1$

Add $- 2$ and $1$ .

$- \frac{5 g}{2} + \frac{1}{4} = - \frac{5 g}{8} - 1$

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

Add $\frac{5 g}{8}$ to both sides of the equation.

$- \frac{5 g}{2} + \frac{1}{4} + \frac{5 g}{8} = - 1$

To write $- \frac{5 g}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{5 g}{2} \cdot \frac{4}{4} + \frac{5 g}{8} + \frac{1}{4} = - 1$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 g}{2}$ by $\frac{4}{4}$ .

$- \frac{5 g \cdot 4}{2 \cdot 4} + \frac{5 g}{8} + \frac{1}{4} = - 1$

Multiply $2$ by $4$ .

$- \frac{5 g \cdot 4}{8} + \frac{5 g}{8} + \frac{1}{4} = - 1$

Combine the numerators over the common denominator.

$\frac{- 5 g \cdot 4 + 5 g}{8} + \frac{1}{4} = - 1$

Simplify each term.

Simplify the numerator.

Factor $5 g$ out of $- 5 g \cdot 4 + 5 g$ .

Factor $5 g$ out of $- 5 g \cdot 4$ .

$\frac{5 g (- 1 \cdot 4) + 5 g}{8} + \frac{1}{4} = - 1$

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

$\frac{5 g (- 1 \cdot 4) + 5 g (1)}{8} + \frac{1}{4} = - 1$

Factor $5 g$ out of $5 g (- 1 \cdot 4) + 5 g (1)$ .

$\frac{5 g (- 1 \cdot 4 + 1)}{8} + \frac{1}{4} = - 1$

Multiply $- 1$ by $4$ .

$\frac{5 g (- 4 + 1)}{8} + \frac{1}{4} = - 1$

Add $- 4$ and $1$ .

$\frac{5 g \cdot - 3}{8} + \frac{1}{4} = - 1$

Multiply $- 3$ by $5$ .

$\frac{- 15 g}{8} + \frac{1}{4} = - 1$

Move the negative in front of the fraction.

$- \frac{15 g}{8} + \frac{1}{4} = - 1$

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

Subtract $\frac{1}{4}$ from both sides of the equation.

$- \frac{15 g}{8} = - 1 - \frac{1}{4}$

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

$- \frac{15 g}{8} = - 1 \cdot \frac{4}{4} - \frac{1}{4}$

Combine $- 1$ and $\frac{4}{4}$ .

$- \frac{15 g}{8} = \frac{- 1 \cdot 4}{4} - \frac{1}{4}$

Combine the numerators over the common denominator.

$- \frac{15 g}{8} = \frac{- 1 \cdot 4 - 1}{4}$

Simplify the numerator.

Multiply $- 1$ by $4$ .

$- \frac{15 g}{8} = \frac{- 4 - 1}{4}$

Subtract $1$ from $- 4$ .

$- \frac{15 g}{8} = \frac{- 5}{4}$

Move the negative in front of the fraction.

$- \frac{15 g}{8} = - \frac{5}{4}$

Multiply both sides of the equation by $- \frac{8}{15}$ .

$- \frac{8}{15} (- \frac{15 g}{8}) = - \frac{8}{15} (- \frac{5}{4})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{8}{15} (- \frac{15 g}{8})$ .

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{8}{15}$ into the numerator.

$\frac{- 8}{15} (- \frac{15 g}{8}) = - \frac{8}{15} (- \frac{5}{4})$

Move the leading negative in $- \frac{15 g}{8}$ into the numerator.

$\frac{- 8}{15} \cdot \frac{- 15 g}{8} = - \frac{8}{15} (- \frac{5}{4})$

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{15} \cdot \frac{- 15 g}{8} = - \frac{8}{15} (- \frac{5}{4})$

Cancel the common factor.

$\frac{8 \cdot - 1}{15} \cdot \frac{- 15 g}{8} = - \frac{8}{15} (- \frac{5}{4})$

Rewrite the expression.

$\frac{- 1}{15} (- 15 g) = - \frac{8}{15} (- \frac{5}{4})$

Cancel the common factor of $15$ .

Factor $15$ out of $- 15 g$ .

$\frac{- 1}{15} (15 (- g)) = - \frac{8}{15} (- \frac{5}{4})$

Cancel the common factor.

$\frac{- 1}{15} (15 (- g)) = - \frac{8}{15} (- \frac{5}{4})$

Rewrite the expression.

$- - g = - \frac{8}{15} (- \frac{5}{4})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 g = - \frac{8}{15} (- \frac{5}{4})$

Multiply $g$ by $1$ .

$g = - \frac{8}{15} (- \frac{5}{4})$

Simplify the right side.

Simplify $- \frac{8}{15} (- \frac{5}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{8}{15}$ into the numerator.

$g = \frac{- 8}{15} (- \frac{5}{4})$

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$g = \frac{- 8}{15} \cdot \frac{- 5}{4}$

Factor $4$ out of $- 8$ .

$g = \frac{4 (- 2)}{15} \cdot \frac{- 5}{4}$

Cancel the common factor.

$g = \frac{4 \cdot - 2}{15} \cdot \frac{- 5}{4}$

Rewrite the expression.

$g = \frac{- 2}{15} \cdot - 5$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

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

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $- 2$ by $- 1$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$g = 0.\overline{6}$

Solve for g -1/2g+1/4-2g=-2-5/8g+1

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