Solve for p -9/10p-3=3/5

$- \frac{9}{10} p - 3 = \frac{3}{5}$

Step 1

Simplify each term.

Combine $p$ and $\frac{9}{10}$ .

$- \frac{p \cdot 9}{10} - 3 = \frac{3}{5}$

Move $9$ to the left of $p$ .

$- \frac{9 p}{10} - 3 = \frac{3}{5}$

Step 2

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

Add $3$ to both sides of the equation.

$- \frac{9 p}{10} = \frac{3}{5} + 3$

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

$- \frac{9 p}{10} = \frac{3}{5} + 3 \cdot \frac{5}{5}$

Combine $3$ and $\frac{5}{5}$ .

$- \frac{9 p}{10} = \frac{3}{5} + \frac{3 \cdot 5}{5}$

Combine the numerators over the common denominator.

$- \frac{9 p}{10} = \frac{3 + 3 \cdot 5}{5}$

Simplify the numerator.

Multiply $3$ by $5$ .

$- \frac{9 p}{10} = \frac{3 + 15}{5}$

Add $3$ and $15$ .

$- \frac{9 p}{10} = \frac{18}{5}$

Step 3

Multiply both sides of the equation by $- \frac{10}{9}$ .

$- \frac{10}{9} (- \frac{9 p}{10}) = - \frac{10}{9} \cdot \frac{18}{5}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{10}{9} (- \frac{9 p}{10})$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{10}{9}$ into the numerator.

$\frac{- 10}{9} (- \frac{9 p}{10}) = - \frac{10}{9} \cdot \frac{18}{5}$

Move the leading negative in $- \frac{9 p}{10}$ into the numerator.

$\frac{- 10}{9} \cdot \frac{- 9 p}{10} = - \frac{10}{9} \cdot \frac{18}{5}$

Factor $10$ out of $- 10$ .

$\frac{10 (- 1)}{9} \cdot \frac{- 9 p}{10} = - \frac{10}{9} \cdot \frac{18}{5}$

Cancel the common factor.

$\frac{10 \cdot - 1}{9} \cdot \frac{- 9 p}{10} = - \frac{10}{9} \cdot \frac{18}{5}$

Rewrite the expression.

$\frac{- 1}{9} (- 9 p) = - \frac{10}{9} \cdot \frac{18}{5}$

Cancel the common factor of $9$ .

Factor $9$ out of $- 9 p$ .

$\frac{- 1}{9} (9 (- p)) = - \frac{10}{9} \cdot \frac{18}{5}$

Cancel the common factor.

$\frac{- 1}{9} (9 (- p)) = - \frac{10}{9} \cdot \frac{18}{5}$

Rewrite the expression.

$- - p = - \frac{10}{9} \cdot \frac{18}{5}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 p = - \frac{10}{9} \cdot \frac{18}{5}$

Multiply $p$ by $1$ .

$p = - \frac{10}{9} \cdot \frac{18}{5}$

Simplify the right side.

Simplify $- \frac{10}{9} \cdot \frac{18}{5}$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{10}{9}$ into the numerator.

$p = \frac{- 10}{9} \cdot \frac{18}{5}$

Factor $5$ out of $- 10$ .

$p = \frac{5 (- 2)}{9} \cdot \frac{18}{5}$

Cancel the common factor.

$p = \frac{5 \cdot - 2}{9} \cdot \frac{18}{5}$

Rewrite the expression.

$p = \frac{- 2}{9} \cdot 18$

Cancel the common factor of $9$ .

Factor $9$ out of $18$ .

$p = \frac{- 2}{9} \cdot (9 (2))$

Cancel the common factor.

$p = \frac{- 2}{9} \cdot (9 \cdot 2)$

Rewrite the expression.

$p = - 2 \cdot 2$

Multiply $- 2$ by $2$ .

$p = - 4$

Solve for p -9/10p-3=3/5

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