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

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

Step 1

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

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

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

Subtract $u$ from both sides of the equation.

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

Step 2

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

Simplify each term.

Apply the distributive property.

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

Multiply $4$ by $1$ .

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

Apply the distributive property.

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

Multiply $- 3$ by $- 1$ .

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

Subtract $3 u$ from $4 u$ .

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

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

Subtract $u$ from $u$ .

$0 + 4 - 7 + 3 = 0$

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