Have one solution, no solution, or infinitely many solutions

2 (x - 3) = 2x

3 (y - 3) = 2y - 9 + y

10x - 2 - 6x = 3x - 2 + x

4 (x + 3) + 2x = x - 8

2 (x - 3) = 2x

Cancel 2 on both sides

x - 3 = x

Cancel x on both sides

-3 = 0

Since - 3 = 0 is false, there is no solution.

3 (y - 3) = 2y - 9 + y

Simplify 2y - 9 + y to 3y - 9

3 (y - 3) = 3y - 9

Expand

3y - 9 = 3y - 9

Since both sides equal, there are infinitely many solutions.

10x - 2 - 6x = 3x - 2 + x

Cancel - 2 on both sides

10x - 6x = 3x + x

Simplify 10x - 6x to 4x

4x = 3x + x

Simplify 3x + x to 4x

4x = 4x

Since both sides equal, there are infinitely many solutions.

4 (x + 3) + 2x = x - 8

Expand

4x + 12 + 2x = x - 8

Simplify 4x + 12 + 2x to 6x + 12

6x + 12 = x - 8

Subtract x from both sides

6x + 12 - x = - 8

Simplify 6x + 12 - x to 5x + 12

5x + 12 = - 8

Subtract 12 from both sides

5x = - 8 - 12

Simplify - 8 - 12 to - 20

5x = - 20

Divide both sides by 5

x = - 20/5

Simplify 20/5 to 4

x = - 4

One solution