3x - 10 = 3(x - 4) + 2

Question

sove the equation    3x - 10 = 3(x - 4) + 2

Answer 1

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.