Solve for x 4(x+1)+x=8(x-1)+6

$4 (x + 1) + x = 8 (x - 1) + 6$

Step 1

Simplify $4 (x + 1) + x$ .

Simplify each term.

Apply the distributive property.

$4 x + 4 \cdot 1 + x = 8 (x - 1) + 6$

Multiply $4$ by $1$ .

$4 x + 4 + x = 8 (x - 1) + 6$

Add $4 x$ and $x$ .

$5 x + 4 = 8 (x - 1) + 6$

Step 2

Simplify $8 (x - 1) + 6$ .

Simplify each term.

Apply the distributive property.

$5 x + 4 = 8 x + 8 \cdot - 1 + 6$

Multiply $8$ by $- 1$ .

$5 x + 4 = 8 x - 8 + 6$

Add $- 8$ and $6$ .

$5 x + 4 = 8 x - 2$

Step 3

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

Subtract $8 x$ from both sides of the equation.

$5 x + 4 - 8 x = - 2$

Subtract $8 x$ from $5 x$ .

$- 3 x + 4 = - 2$

Step 4

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

Subtract $4$ from both sides of the equation.

$- 3 x = - 2 - 4$

Subtract $4$ from $- 2$ .

$- 3 x = - 6$

Step 5

Divide each term in $- 3 x = - 6$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 6$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 6}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$x = 2$