Solve for q 1/2-1/8q=(q-1)/4

$\frac{1}{2} - \frac{1}{8} q = \frac{q - 1}{4}$

Multiply both sides by $4$ .

$(\frac{1}{2} - \frac{1}{8} q) \cdot 4 = \frac{q - 1}{4} \cdot 4$

Simplify.

Simplify the left side.

Simplify $(\frac{1}{2} - \frac{1}{8} q) \cdot 4$ .

Combine $q$ and $\frac{1}{8}$ .

$(\frac{1}{2} - \frac{q}{8}) \cdot 4 = \frac{q - 1}{4} \cdot 4$

Apply the distributive property.

$\frac{1}{2} \cdot 4 - \frac{q}{8} \cdot 4 = \frac{q - 1}{4} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{1}{2} \cdot (2 (2)) - \frac{q}{8} \cdot 4 = \frac{q - 1}{4} \cdot 4$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 2) - \frac{q}{8} \cdot 4 = \frac{q - 1}{4} \cdot 4$

Rewrite the expression.

$2 - \frac{q}{8} \cdot 4 = \frac{q - 1}{4} \cdot 4$

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $8$ .

$2 + \frac{- q}{4 (2)} \cdot 4 = \frac{q - 1}{4} \cdot 4$

Cancel the common factor.

$2 + \frac{- q}{4 \cdot 2} \cdot 4 = \frac{q - 1}{4} \cdot 4$

Rewrite the expression.

$2 + \frac{- q}{2} = \frac{q - 1}{4} \cdot 4$

Simplify the expression.

Move the negative in front of the fraction.

$2 - \frac{q}{2} = \frac{q - 1}{4} \cdot 4$

Reorder $2$ and $- \frac{q}{2}$ .

$- \frac{q}{2} + 2 = \frac{q - 1}{4} \cdot 4$

Simplify the right side.

Cancel the common factor of $4$ .

Cancel the common factor.

$- \frac{q}{2} + 2 = \frac{q - 1}{4} \cdot 4$

Rewrite the expression.

$- \frac{q}{2} + 2 = q - 1$

Solve for $q$ .

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

Subtract $q$ from both sides of the equation.

$- \frac{q}{2} + 2 - q = - 1$

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

$- \frac{q}{2} - q \cdot \frac{2}{2} + 2 = - 1$

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

$- \frac{q}{2} + \frac{- q \cdot 2}{2} + 2 = - 1$

Combine the numerators over the common denominator.

$\frac{- q - q \cdot 2}{2} + 2 = - 1$

Simplify each term.

Simplify the numerator.

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

Factor $q$ out of $- q$ .

$\frac{q \cdot - 1 - q \cdot 2}{2} + 2 = - 1$

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

$\frac{q \cdot - 1 + q (- 1 \cdot 2)}{2} + 2 = - 1$

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

$\frac{q (- 1 - 1 \cdot 2)}{2} + 2 = - 1$

Multiply $- 1$ by $2$ .

$\frac{q (- 1 - 2)}{2} + 2 = - 1$

Subtract $2$ from $- 1$ .

$\frac{q \cdot - 3}{2} + 2 = - 1$

Move $- 3$ to the left of $q$ .

$\frac{- 3 \cdot q}{2} + 2 = - 1$

Move the negative in front of the fraction.

$- \frac{3 q}{2} + 2 = - 1$

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

Subtract $2$ from both sides of the equation.

$- \frac{3 q}{2} = - 1 - 2$

Subtract $2$ from $- 1$ .

$- \frac{3 q}{2} = - 3$

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{3} (- \frac{3 q}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 q}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 q}{2} = - \frac{2}{3} \cdot - 3$

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 q$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - q = - \frac{2}{3} \cdot - 3$

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $q$ by $1$ .

$q = - \frac{2}{3} \cdot - 3$

Simplify the right side.

Simplify $- \frac{2}{3} \cdot - 3$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$q = \frac{- 2}{3} \cdot - 3$

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$q = - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$q = 2$

Solve for q 1/2-1/8q=(q-1)/4

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