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

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

Step 1

Simplify $- 1 - 2 p + \frac{1}{3} p$ .

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

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

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

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

Simplify terms.

Combine $- 2 p$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

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

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

Raise $p$ to the power of $1$ .

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

Factor $p$ out of $p^{1}$ .

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

Factor $p$ out of $p (- 2 \cdot 3) + p \cdot 1$ .

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

Multiply $- 2$ by $3$ .

$- 1 + \frac{p (- 6 + 1)}{3} = - \frac{3}{2} p + 2$

Add $- 6$ and $1$ .

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

Move $- 5$ to the left of $p$ .

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

Move the negative in front of the fraction.

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

Step 2

Simplify each term.

Combine $p$ and $\frac{3}{2}$ .

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

Move $3$ to the left of $p$ .

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

Step 3

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

Add $\frac{3 p}{2}$ to both sides of the equation.

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

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

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

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

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $2$ .

$- 1 - \frac{5 p \cdot 2}{6} + \frac{3 p}{2} \cdot \frac{3}{3} = 2$

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

$- 1 - \frac{5 p \cdot 2}{6} + \frac{3 p \cdot 3}{2 \cdot 3} = 2$

Multiply $2$ by $3$ .

$- 1 - \frac{5 p \cdot 2}{6} + \frac{3 p \cdot 3}{6} = 2$

Combine the numerators over the common denominator.

$- 1 + \frac{- 5 p \cdot 2 + 3 p \cdot 3}{6} = 2$

Simplify each term.

Simplify the numerator.

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

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

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

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

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

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

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

Multiply $- 5$ by $2$ .

$- 1 + \frac{p (- 10 + 3 \cdot 3)}{6} = 2$

Multiply $3$ by $3$ .

$- 1 + \frac{p (- 10 + 9)}{6} = 2$

Add $- 10$ and $9$ .

$- 1 + \frac{p \cdot - 1}{6} = 2$

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

$- 1 + \frac{- 1 \cdot p}{6} = 2$

Move the negative in front of the fraction.

$- 1 - \frac{p}{6} = 2$

Step 4

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

Add $1$ to both sides of the equation.

$- \frac{p}{6} = 2 + 1$

Add $2$ and $1$ .

$- \frac{p}{6} = 3$

Step 5

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{p}{6}) = - 6 \cdot 3$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 6 (- \frac{p}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{p}{6}$ into the numerator.

$- 6 \frac{- p}{6} = - 6 \cdot 3$

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- p}{6} = - 6 \cdot 3$

Cancel the common factor.

$6 \cdot - 1 \frac{- p}{6} = - 6 \cdot 3$

Rewrite the expression.

$- - p = - 6 \cdot 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 p = - 6 \cdot 3$

Multiply $p$ by $1$ .

$p = - 6 \cdot 3$

Simplify the right side.

Multiply $- 6$ by $3$ .

$p = - 18$

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

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