Solve for p -2/5p+2=1/5p+11

$- \frac{2}{5} p + 2 = \frac{1}{5} p + 11$

Step 1

Simplify each term.

Combine $p$ and $\frac{2}{5}$ .

$- \frac{p \cdot 2}{5} + 2 = \frac{1}{5} p + 11$

Move $2$ to the left of $p$ .

$- \frac{2 p}{5} + 2 = \frac{1}{5} p + 11$

Step 2

Combine $\frac{1}{5}$ and $p$ .

$- \frac{2 p}{5} + 2 = \frac{p}{5} + 11$

Step 3

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

Subtract $\frac{p}{5}$ from both sides of the equation.

$- \frac{2 p}{5} + 2 - \frac{p}{5} = 11$

Combine the numerators over the common denominator.

$2 + \frac{- 2 p - p}{5} = 11$

Subtract $p$ from $- 2 p$ .

$2 + \frac{- 3 p}{5} = 11$

Move the negative in front of the fraction.

$2 - \frac{3 p}{5} = 11$

Step 4

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

Subtract $2$ from both sides of the equation.

$- \frac{3 p}{5} = 11 - 2$

Subtract $2$ from $11$ .

$- \frac{3 p}{5} = 9$

Step 5

Multiply both sides of the equation by $- \frac{5}{3}$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{3} (- \frac{3 p}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 p}{5}$ into the numerator.

$\frac{- 5}{3} \cdot \frac{- 3 p}{5} = - \frac{5}{3} \cdot 9$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{3} \cdot \frac{- 3 p}{5} = - \frac{5}{3} \cdot 9$

Cancel the common factor.

$\frac{5 \cdot - 1}{3} \cdot \frac{- 3 p}{5} = - \frac{5}{3} \cdot 9$

Rewrite the expression.

$\frac{- 1}{3} (- 3 p) = - \frac{5}{3} \cdot 9$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 p$ .

$\frac{- 1}{3} (3 (- p)) = - \frac{5}{3} \cdot 9$

Cancel the common factor.

$\frac{- 1}{3} (3 (- p)) = - \frac{5}{3} \cdot 9$

Rewrite the expression.

$- - p = - \frac{5}{3} \cdot 9$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 p = - \frac{5}{3} \cdot 9$

Multiply $p$ by $1$ .

$p = - \frac{5}{3} \cdot 9$

Simplify the right side.

Simplify $- \frac{5}{3} \cdot 9$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$p = \frac{- 5}{3} \cdot 9$

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$p = - 5 \cdot 3$

Multiply $- 5$ by $3$ .

$p = - 15$

Solve for p -2/5p+2=1/5p+11

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