sove the equation 3x - 10 = 3(x - 4) + 2
Distribute the 3 on the right side, to get
3x - 10 = 3x - 12 + 2.
Simplify on the right, and we get
3x - 10 = 3x - 10
Collecting like terms (moving 3x from right to left and -10 from left to right) we get
0 = 0
Now, this is a true statement - zero always equals zero, regardless of the value of x we pick. Therefore, x can be all real numbers.
In contrast, if the result was
0 = 1 (or any two numbers that were NOT the same)
then there would be NO SOLUTION, because zero does not equal one, and 0 = 1 is a false statement.