Solve for q 2(q+p)=1+5q

$2 (q + p) = 1 + 5 q$

Step 1

Simplify $2 (q + p)$ .

Rewrite.

$0 + 0 + 2 (q + p) = 1 + 5 q$

Simplify by adding zeros.

$2 (q + p) = 1 + 5 q$

Apply the distributive property.

$2 q + 2 p = 1 + 5 q$

Step 2

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

Subtract $5 q$ from both sides of the equation.

$2 q + 2 p - 5 q = 1$

Subtract $5 q$ from $2 q$ .

$2 p - 3 q = 1$

Step 3

Subtract $2 p$ from both sides of the equation.

$- 3 q = 1 - 2 p$

Step 4

Divide each term in $- 3 q = 1 - 2 p$ by $- 3$ and simplify.

Divide each term in $- 3 q = 1 - 2 p$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $q$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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