Question

Describe how you know whether an equation will be true for all values of x or true for no values of x

Answer 1

Explanation:

Generally an equation which will be true for all values of x have some statement which can be simplified into another state which will always be true.

So for example:
`x+4=x+4`, is kind of a bit obvious to tell it's going to be true for all values as the two expressions have the same exact terms, but we can subtract "x" from both sides leading us to the statement:
`4=4` which is always true.

One important thing to note is you must be cautious at times, for example:
`(x-2)/(x-2)=(x-2)/(x-2)` may seem to be true for all values, and x-2 over x-2 is the same thing, so it simplifies to one and same thing on the right side:
`1=1` thus the statement should be true for all values right? Not completely, it's true for most values, except for x=2, and this is because 1=1 isn't exactly the same expression. In the original fraction the denominator has an x-2, and if we plug in x=2, we get 2-2 resulting in division by one, which of course isn't definable. So that's just one important thing to note as simplifying expressions may result in expressions that look equal, but are slightly different in a way.