Solve for p 1/3p=2/5p+2/3

$\frac{1}{3} p = \frac{2}{5} p + \frac{2}{3}$

Step 1

Simplify $\frac{1}{3} p$ .

Rewrite.

$0 + 0 + \frac{1}{3} p = \frac{2}{5} p + \frac{2}{3}$

Simplify by adding zeros.

$\frac{1}{3} p = \frac{2}{5} p + \frac{2}{3}$

Combine $\frac{1}{3}$ and $p$ .

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

Step 2

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

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

Step 3

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

Subtract $\frac{2 p}{5}$ from both sides of the equation.

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

To write $\frac{p}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

To write $- \frac{2 p}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{p}{3}$ by $\frac{5}{5}$ .

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

Multiply $3$ by $5$ .

$\frac{p \cdot 5}{15} - \frac{2 p}{5} \cdot \frac{3}{3} = \frac{2}{3}$

Multiply $\frac{2 p}{5}$ by $\frac{3}{3}$ .

$\frac{p \cdot 5}{15} - \frac{2 p \cdot 3}{5 \cdot 3} = \frac{2}{3}$

Multiply $5$ by $3$ .

$\frac{p \cdot 5}{15} - \frac{2 p \cdot 3}{15} = \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{p \cdot 5 - 2 p \cdot 3}{15} = \frac{2}{3}$

Simplify the numerator.

Factor $p$ out of $p \cdot 5 - 2 p \cdot 3$ .

Factor $p$ out of $p \cdot 5$ .

$\frac{p (5) - 2 p \cdot 3}{15} = \frac{2}{3}$

Factor $p$ out of $- 2 p \cdot 3$ .

$\frac{p (5) + p (- 2 \cdot 3)}{15} = \frac{2}{3}$

Factor $p$ out of $p (5) + p (- 2 \cdot 3)$ .

$\frac{p (5 - 2 \cdot 3)}{15} = \frac{2}{3}$

Multiply $- 2$ by $3$ .

$\frac{p (5 - 6)}{15} = \frac{2}{3}$

Subtract $6$ from $5$ .

$\frac{p \cdot - 1}{15} = \frac{2}{3}$

Move $- 1$ to the left of $p$ .

$\frac{- 1 \cdot p}{15} = \frac{2}{3}$

Move the negative in front of the fraction.

$- \frac{p}{15} = \frac{2}{3}$

Step 4

Multiply both sides of the equation by $- 15$ .

$- 15 (- \frac{p}{15}) = - 15 (\frac{2}{3})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 15 (- \frac{p}{15})$ .

Cancel the common factor of $15$ .

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

$- 15 \frac{- p}{15} = - 15 (\frac{2}{3})$

Factor $15$ out of $- 15$ .

$15 (- 1) \frac{- p}{15} = - 15 (\frac{2}{3})$

Cancel the common factor.

$15 \cdot - 1 \frac{- p}{15} = - 15 (\frac{2}{3})$

Rewrite the expression.

$- - p = - 15 (\frac{2}{3})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 p = - 15 (\frac{2}{3})$

Multiply $p$ by $1$ .

$p = - 15 (\frac{2}{3})$

Simplify the right side.

Simplify $- 15 (\frac{2}{3})$ .

Cancel the common factor of $3$ .

Factor $3$ out of $- 15$ .

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

Cancel the common factor.

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

Rewrite the expression.

$p = - 5 \cdot 2$

Multiply $- 5$ by $2$ .

$p = - 10$

Solve for p 1/3p=2/5p+2/3

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