Solve for p 1/3(p+9)=3+2(p-6)

$\frac{1}{3} (p + 9) = 3 + 2 (p - 6)$

Step 1

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

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (p + 9) = 3 + 2 (p - 6)$

Simplify by adding zeros.

$\frac{1}{3} \cdot (p + 9) = 3 + 2 (p - 6)$

Apply the distributive property.

$\frac{1}{3} p + \frac{1}{3} \cdot 9 = 3 + 2 (p - 6)$

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

$\frac{p}{3} + \frac{1}{3} \cdot 9 = 3 + 2 (p - 6)$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify $3 + 2 (p - 6)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 6$ .

$\frac{p}{3} + 3 = 3 + 2 p - 12$

Subtract $12$ from $3$ .

$\frac{p}{3} + 3 = 2 p - 9$

Step 3

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

Subtract $2 p$ from both sides of the equation.

$\frac{p}{3} + 3 - 2 p = - 9$

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

$\frac{p}{3} - 2 p \cdot \frac{3}{3} + 3 = - 9$

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

$\frac{p}{3} + \frac{- 2 p \cdot 3}{3} + 3 = - 9$

Combine the numerators over the common denominator.

$\frac{p - 2 p \cdot 3}{3} + 3 = - 9$

Simplify each term.

Simplify the numerator.

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

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

$\frac{p^{1} - 2 p \cdot 3}{3} + 3 = - 9$

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

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

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

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

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

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

Multiply $- 2$ by $3$ .

$\frac{p (1 - 6)}{3} + 3 = - 9$

Subtract $6$ from $1$ .

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

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

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

Move the negative in front of the fraction.

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

Step 4

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

Subtract $3$ from both sides of the equation.

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

Subtract $3$ from $- 9$ .

$- \frac{5 p}{3} = - 12$

Step 5

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

$- \frac{3}{5} (- \frac{5 p}{3}) = - \frac{3}{5} \cdot - 12$

Step 6

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

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

$\frac{- 3}{5} (- \frac{5 p}{3}) = - \frac{3}{5} \cdot - 12$

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

$\frac{- 3}{5} \cdot \frac{- 5 p}{3} = - \frac{3}{5} \cdot - 12$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{5} \cdot \frac{- 5 p}{3} = - \frac{3}{5} \cdot - 12$

Cancel the common factor.

$\frac{3 \cdot - 1}{5} \cdot \frac{- 5 p}{3} = - \frac{3}{5} \cdot - 12$

Rewrite the expression.

$\frac{- 1}{5} (- 5 p) = - \frac{3}{5} \cdot - 12$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 p$ .

$\frac{- 1}{5} (5 (- p)) = - \frac{3}{5} \cdot - 12$

Cancel the common factor.

$\frac{- 1}{5} (5 (- p)) = - \frac{3}{5} \cdot - 12$

Rewrite the expression.

$- - p = - \frac{3}{5} \cdot - 12$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 p = - \frac{3}{5} \cdot - 12$

Multiply $p$ by $1$ .

$p = - \frac{3}{5} \cdot - 12$

Simplify the right side.

Multiply $- \frac{3}{5} \cdot - 12$ .

Multiply $- 12$ by $- 1$ .

$p = 12 (\frac{3}{5})$

Combine $12$ and $\frac{3}{5}$ .

$p = \frac{12 \cdot 3}{5}$

Multiply $12$ by $3$ .

$p = \frac{36}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$p = \frac{36}{5}$

Decimal Form:

$p = 7.2$

Mixed Number Form:

$p = 7 \frac{1}{5}$

Solve for p 1/3(p+9)=3+2(p-6)

Related Questions

Support LCMGCF.com by disabling your adblocker.