How do you solve 5x-2 equals 5x-2?

Answer 1

It's a trivial truism, true for any value of 'x'.

If you're trying to solve the equation, you have to stop for a moment and

remember what "solve" means.

The "solution" to an equation is the number that you can put in place of 'x'

and make the statement true. Sometimes there's only one number, sometimes

2 or 3 or more. But it's always a limited number of "solutions", and you can

write them down in a list. Any number that's not on the list is not a solution

of the equation.

That's not the situation with this one. This statement is always true, no matter

what number you stick in place of 'x'. Try it.

Pick a number, any number. I pick 1,492. Watch what happens when I put it in place of 'x':

5 (1,492) - 2 = 5 (1,492) - 2

7,460 - 2 = 7,460 - 2

7,458 = 7,458 That's a true statement.

The equation is called "trivial" because every number that was ever invented

or that anybody ever thought about in the history of math is a solution to the

equation. It's impossible to find any number that's not a solution. So you

don't have to do anything to solve it. Just pick any number out of thin air

and you have one solution.

But you'll never be able to list all the solutions. And until you do that, you can't

say that you've completely "solved" it.