Solve by Factoring 3(x+1)+2x=5(x-1)+5

$3 (x + 1) + 2 x = 5 (x - 1) + 5$

Step 1

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

Subtract $5 (x - 1)$ from both sides of the equation.

$3 (x + 1) + 2 x - 5 (x - 1) = 5$

Subtract $5$ from both sides of the equation.

$3 (x + 1) + 2 x - 5 (x - 1) - 5 = 0$

Step 2

Simplify $3 (x + 1) + 2 x - 5 (x - 1) - 5$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 1 + 2 x - 5 (x - 1) - 5 = 0$

Multiply $3$ by $1$ .

$3 x + 3 + 2 x - 5 (x - 1) - 5 = 0$

Apply the distributive property.

$3 x + 3 + 2 x - 5 x - 5 \cdot - 1 - 5 = 0$

Multiply $- 5$ by $- 1$ .

$3 x + 3 + 2 x - 5 x + 5 - 5 = 0$

Combine the opposite terms in $3 x + 3 + 2 x - 5 x + 5 - 5$ .

Subtract $5$ from $5$ .

$3 x + 3 + 2 x - 5 x + 0 = 0$

Add $3 x + 3 + 2 x - 5 x$ and $0$ .

$3 x + 3 + 2 x - 5 x = 0$

Add $3 x$ and $2 x$ .

$5 x + 3 - 5 x = 0$

Combine the opposite terms in $5 x + 3 - 5 x$ .

Subtract $5 x$ from $5 x$ .

$0 + 3 = 0$

Add $0$ and $3$ .

$3 = 0$

Step 3

Since $3 \neq 0$ , there are no solutions.

No solution