Question

How many solutions are there to the following equation ? 12x + 5 = 12x - 19

Answer 1

No solution because 12x and 12x rule each other out because 12x-12x is 0
You are left with 5=-19
And obviously 5 does not equal -19
So it is no solution

Answer 2

0, no solutions

Explanation:

There are 2 ways to solve this equation. The first is to use the properties of equality to solve for x.

To do this first subtract 5 from both sides

12x=12x-24

Then, divide both sides by 12x

0=-24

This is obviously an untrue statement and therefore there are no solutions.

Additionally, in the equation different operations, +5 and -12, are happening to the same number, 12x. This means that it is impossible to have any solutions. Logic can tell you that no number is equal when 5 is added and when 12 is subtracted.