Solve for q (8q-2)/12-6=(10q+6)/6

$\frac{8 q - 2}{12} - 6 = \frac{10 q + 6}{6}$

Step 1

Cancel the common factor of $10 q + 6$ and $6$ .

Factor $2$ out of $10 q$ .

$\frac{8 q - 2}{12} - 6 = \frac{2 (5 q) + 6}{6}$

Factor $2$ out of $6$ .

$\frac{8 q - 2}{12} - 6 = \frac{2 (5 q) + 2 (3)}{6}$

Factor $2$ out of $2 (5 q) + 2 (3)$ .

$\frac{8 q - 2}{12} - 6 = \frac{2 (5 q + 3)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{8 q - 2}{12} - 6 = \frac{2 (5 q + 3)}{2 (3)}$

Cancel the common factor.

$\frac{8 q - 2}{12} - 6 = \frac{2 (5 q + 3)}{2 \cdot 3}$

Rewrite the expression.

$\frac{8 q - 2}{12} - 6 = \frac{5 q + 3}{3}$

Step 2

Multiply both sides by $3$ .

$(\frac{8 q - 2}{12} - 6) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Step 3

Simplify.

Simplify the left side.

Simplify $(\frac{8 q - 2}{12} - 6) \cdot 3$ .

Cancel the common factor of $8 q - 2$ and $12$ .

Factor $2$ out of $8 q$ .

$(\frac{2 (4 q) - 2}{12} - 6) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Factor $2$ out of $- 2$ .

$(\frac{2 (4 q) + 2 (- 1)}{12} - 6) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Factor $2$ out of $2 (4 q) + 2 (- 1)$ .

$(\frac{2 (4 q - 1)}{12} - 6) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Cancel the common factors.

Factor $2$ out of $12$ .

$(\frac{2 (4 q - 1)}{2 (6)} - 6) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Cancel the common factor.

$(\frac{2 (4 q - 1)}{2 \cdot 6} - 6) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Rewrite the expression.

$(\frac{4 q - 1}{6} - 6) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

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

$(\frac{4 q - 1}{6} - 6 \cdot \frac{6}{6}) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Simplify terms.

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

$(\frac{4 q - 1}{6} + \frac{- 6 \cdot 6}{6}) \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Combine the numerators over the common denominator.

$\frac{4 q - 1 - 6 \cdot 6}{6} \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Simplify the numerator.

Multiply $- 6$ by $6$ .

$\frac{4 q - 1 - 36}{6} \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Subtract $36$ from $- 1$ .

$\frac{4 q - 37}{6} \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{4 q - 37}{3 (2)} \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Cancel the common factor.

$\frac{4 q - 37}{3 \cdot 2} \cdot 3 = \frac{5 q + 3}{3} \cdot 3$

Rewrite the expression.

$\frac{4 q - 37}{2} = \frac{5 q + 3}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4 q - 37}{2} = \frac{5 q + 3}{3} \cdot 3$

Rewrite the expression.

$\frac{4 q - 37}{2} = 5 q + 3$

Step 4

Solve for $q$ .

Multiply both sides by $2$ .

$\frac{4 q - 37}{2} \cdot 2 = (5 q + 3) \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 q - 37}{2} \cdot 2 = (5 q + 3) \cdot 2$

Rewrite the expression.

$4 q - 37 = (5 q + 3) \cdot 2$

Simplify the right side.

Simplify $(5 q + 3) \cdot 2$ .

Apply the distributive property.

$4 q - 37 = 5 q \cdot 2 + 3 \cdot 2$

Multiply.

Multiply $2$ by $5$ .

$4 q - 37 = 10 q + 3 \cdot 2$

Multiply $3$ by $2$ .

$4 q - 37 = 10 q + 6$

Solve for $q$ .

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

Subtract $10 q$ from both sides of the equation.

$4 q - 37 - 10 q = 6$

Subtract $10 q$ from $4 q$ .

$- 6 q - 37 = 6$

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

Add $37$ to both sides of the equation.

$- 6 q = 6 + 37$

Add $6$ and $37$ .

$- 6 q = 43$

Divide each term in $- 6 q = 43$ by $- 6$ and simplify.

Divide each term in $- 6 q = 43$ by $- 6$ .

$\frac{- 6 q}{- 6} = \frac{43}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 q}{- 6} = \frac{43}{- 6}$

Divide $q$ by $1$ .

$q = \frac{43}{- 6}$

Simplify the right side.

Move the negative in front of the fraction.

$q = - \frac{43}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$q = - \frac{43}{6}$

Decimal Form:

$q = - 7.1\overline{6}$

Mixed Number Form:

$q = - 7 \frac{1}{6}$

Solve for q (8q-2)/12-6=(10q+6)/6

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