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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $1$ .

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

Apply the distributive property.

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

Multiply $8$ by $- 1$ .

$2 x + 2 + 8 x - 8 = 5 x$

Simplify by adding terms.

Add $2 x$ and $8 x$ .

$10 x + 2 - 8 = 5 x$

Subtract $8$ from $2$ .

$10 x - 6 = 5 x$

Step 2

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

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

$10 x - 6 - 5 x = 0$

Subtract $5 x$ from $10 x$ .

$5 x - 6 = 0$

Step 3

Add $6$ to both sides of the equation.

$5 x = 6$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.2$

Mixed Number Form:

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