Solve by Factoring 4(x+1)-7=3(x-1)+x

$4 (x + 1) - 7 = 3 (x - 1) + x$

Step 1

Move all the expressions to the left side of the equation.

Subtract $3 (x - 1)$ from both sides of the equation.

$4 (x + 1) - 7 - 3 (x - 1) = x$

Subtract $x$ from both sides of the equation.

$4 (x + 1) - 7 - 3 (x - 1) - x = 0$

Step 2

Simplify $4 (x + 1) - 7 - 3 (x - 1) - x$ .

Simplify each term.

Apply the distributive property.

$4 x + 4 \cdot 1 - 7 - 3 (x - 1) - x = 0$

Multiply $4$ by $1$ .

$4 x + 4 - 7 - 3 (x - 1) - x = 0$

Apply the distributive property.

$4 x + 4 - 7 - 3 x - 3 \cdot - 1 - x = 0$

Multiply $- 3$ by $- 1$ .

$4 x + 4 - 7 - 3 x + 3 - x = 0$

Subtract $3 x$ from $4 x$ .

$x + 4 - 7 + 3 - x = 0$

Combine the opposite terms in $x + 4 - 7 + 3 - x$ .

Subtract $x$ from $x$ .

$0 + 4 - 7 + 3 = 0$

Add $0$ and $4$ .

$4 - 7 + 3 = 0$

Subtract $7$ from $4$ .

$- 3 + 3 = 0$

Add $- 3$ and $3$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true