Solve by Factoring 2x-6=3x+1-x-7

$2 x - 6 = 3 x + 1 - x - 7$

Step 1

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

Subtract $3 x$ from both sides of the equation.

$2 x - 6 - 3 x = 1 - x - 7$

Subtract $1$ from both sides of the equation.

$2 x - 6 - 3 x - 1 = - x - 7$

Add $x$ to both sides of the equation.

$2 x - 6 - 3 x - 1 + x = - 7$

Add $7$ to both sides of the equation.

$2 x - 6 - 3 x - 1 + x + 7 = 0$

Step 2

Simplify $2 x - 6 - 3 x - 1 + x + 7$ .

Subtract $3 x$ from $2 x$ .

$- x - 6 - 1 + x + 7 = 0$

Combine the opposite terms in $- x - 6 - 1 + x + 7$ .

Add $- x$ and $x$ .

$0 - 6 - 1 + 7 = 0$

Subtract $6$ from $0$ .

$- 6 - 1 + 7 = 0$

Subtract $1$ from $- 6$ .

$- 7 + 7 = 0$

Add $- 7$ and $7$ .

$0 = 0$

Step 3

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

Always true