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

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

Step 1

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

Subtract $2 (x - 1)$ from both sides of the equation.

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

Subtract $5$ from both sides of the equation.

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

Step 2

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

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $2$ .

$3 x + 6 - x - 2 (x - 1) - 5 = 0$

Apply the distributive property.

$3 x + 6 - x - 2 x - 2 \cdot - 1 - 5 = 0$

Multiply $- 2$ by $- 1$ .

$3 x + 6 - x - 2 x + 2 - 5 = 0$

Subtract $x$ from $3 x$ .

$2 x + 6 - 2 x + 2 - 5 = 0$

Combine the opposite terms in $2 x + 6 - 2 x + 2 - 5$ .

Subtract $2 x$ from $2 x$ .

$0 + 6 + 2 - 5 = 0$

Add $0$ and $6$ .

$6 + 2 - 5 = 0$

Add $6$ and $2$ .

$8 - 5 = 0$

Subtract $5$ from $8$ .

$3 = 0$

Step 3

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

No solution