Solve for x 2x-6=3x+1-x-7

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

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

Subtract $x$ from $3 x$ .

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

Subtract $7$ from $1$ .

$2 x - 6 = 2 x - 6$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$2 x - 6 - 2 x = - 6$

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

Subtract $2 x$ from $2 x$ .

$0 - 6 = - 6$

Subtract $6$ from $0$ .

$- 6 = - 6$

Step 4

Since $- 6 = - 6$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$