Solve for p 2(p+1)+8(p-1)=5p

$2 (p + 1) + 8 (p - 1) = 5 p$

Step 1

Simplify $2 (p + 1) + 8 (p - 1)$ .

Simplify each term.

Apply the distributive property.

$2 p + 2 \cdot 1 + 8 (p - 1) = 5 p$

Multiply $2$ by $1$ .

$2 p + 2 + 8 (p - 1) = 5 p$

Apply the distributive property.

$2 p + 2 + 8 p + 8 \cdot - 1 = 5 p$

Multiply $8$ by $- 1$ .

$2 p + 2 + 8 p - 8 = 5 p$

Simplify by adding terms.

Add $2 p$ and $8 p$ .

$10 p + 2 - 8 = 5 p$

Subtract $8$ from $2$ .

$10 p - 6 = 5 p$

Step 2

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

Subtract $5 p$ from both sides of the equation.

$10 p - 6 - 5 p = 0$

Subtract $5 p$ from $10 p$ .

$5 p - 6 = 0$

Step 3

Add $6$ to both sides of the equation.

$5 p = 6$

Step 4

Divide each term in $5 p = 6$ by $5$ and simplify.

Divide each term in $5 p = 6$ by $5$ .

$\frac{5 p}{5} = \frac{6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 p}{5} = \frac{6}{5}$

Divide $p$ by $1$ .

$p = \frac{6}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = \frac{6}{5}$

Decimal Form:

$p = 1.2$

Mixed Number Form:

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