Solve for p 1/3(p-9)=4(p+2)

$\frac{1}{3} (p - 9) = 4 (p + 2)$

Step 1

Simplify $\frac{1}{3} \cdot (p - 9)$ .

Start simplifying.

$0 + 0 + \frac{1}{3} \cdot (p - 9) = 4 (p + 2)$

Simplify by adding zeros.

$\frac{1}{3} \cdot (p - 9) = 4 (p + 2)$

Apply the distributive property.

$\frac{1}{3} p + \frac{1}{3} \cdot - 9 = 4 (p + 2)$

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

$\frac{p}{3} + \frac{1}{3} \cdot - 9 = 4 (p + 2)$

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

$\frac{p}{3} + \frac{1}{3} \cdot (3 (- 3)) = 4 (p + 2)$

Cancel the common factor.

$\frac{p}{3} + \frac{1}{3} \cdot (3 \cdot - 3) = 4 (p + 2)$

Rewrite the expression.

$\frac{p}{3} - 3 = 4 (p + 2)$

Step 2

Simplify $4 (p + 2)$ .

Apply the distributive property.

$\frac{p}{3} - 3 = 4 p + 4 \cdot 2$

Multiply $4$ by $2$ .

$\frac{p}{3} - 3 = 4 p + 8$

Step 3

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

Subtract $4 p$ from both sides of the equation.

$\frac{p}{3} - 3 - 4 p = 8$

To write $- 4 p$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{p}{3} - 4 p \cdot \frac{3}{3} - 3 = 8$

Combine $- 4 p$ and $\frac{3}{3}$ .

$\frac{p}{3} + \frac{- 4 p \cdot 3}{3} - 3 = 8$

Combine the numerators over the common denominator.

$\frac{p - 4 p \cdot 3}{3} - 3 = 8$

Simplify each term.

Simplify the numerator.

Factor $p$ out of $p - 4 p \cdot 3$ .

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

$\frac{p^{1} - 4 p \cdot 3}{3} - 3 = 8$

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

$\frac{p \cdot 1 - 4 p \cdot 3}{3} - 3 = 8$

Factor $p$ out of $- 4 p \cdot 3$ .

$\frac{p \cdot 1 + p (- 4 \cdot 3)}{3} - 3 = 8$

Factor $p$ out of $p \cdot 1 + p (- 4 \cdot 3)$ .

$\frac{p (1 - 4 \cdot 3)}{3} - 3 = 8$

Multiply $- 4$ by $3$ .

$\frac{p (1 - 12)}{3} - 3 = 8$

Subtract $12$ from $1$ .

$\frac{p \cdot - 11}{3} - 3 = 8$

Move $- 11$ to the left of $p$ .

$\frac{- 11 \cdot p}{3} - 3 = 8$

Move the negative in front of the fraction.

$- \frac{11 p}{3} - 3 = 8$

Step 4

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

Add $3$ to both sides of the equation.

$- \frac{11 p}{3} = 8 + 3$

Add $8$ and $3$ .

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

Step 5

Multiply both sides of the equation by $- \frac{3}{11}$ .

$- \frac{3}{11} (- \frac{11 p}{3}) = - \frac{3}{11} \cdot 11$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{11} (- \frac{11 p}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{11}$ into the numerator.

$\frac{- 3}{11} (- \frac{11 p}{3}) = - \frac{3}{11} \cdot 11$

Move the leading negative in $- \frac{11 p}{3}$ into the numerator.

$\frac{- 3}{11} \cdot \frac{- 11 p}{3} = - \frac{3}{11} \cdot 11$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{11} \cdot \frac{- 11 p}{3} = - \frac{3}{11} \cdot 11$

Cancel the common factor.

$\frac{3 \cdot - 1}{11} \cdot \frac{- 11 p}{3} = - \frac{3}{11} \cdot 11$

Rewrite the expression.

$\frac{- 1}{11} (- 11 p) = - \frac{3}{11} \cdot 11$

Cancel the common factor of $11$ .

Factor $11$ out of $- 11 p$ .

$\frac{- 1}{11} (11 (- p)) = - \frac{3}{11} \cdot 11$

Cancel the common factor.

$\frac{- 1}{11} (11 (- p)) = - \frac{3}{11} \cdot 11$

Rewrite the expression.

$- - p = - \frac{3}{11} \cdot 11$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 p = - \frac{3}{11} \cdot 11$

Multiply $p$ by $1$ .

$p = - \frac{3}{11} \cdot 11$

Simplify the right side.

Cancel the common factor of $11$ .

Move the leading negative in $- \frac{3}{11}$ into the numerator.

$p = \frac{- 3}{11} \cdot 11$

Cancel the common factor.

$p = \frac{- 3}{11} \cdot 11$

Rewrite the expression.

$p = - 3$

Solve for p 1/3(p-9)=4(p+2)

Related Questions

Support LCMGCF.com by disabling your adblocker.