how to determine whether an equation is always, sometimes , or never true

Question

nory · Answer

If you try to solve the equation and one of the variables is suddenly eliminated, then you can see if it results in a true or false statement.

anonymous · Answer

Start by simplifying both sides and then try plugging in different values to test it.

nory · Answer

For example 2x + 4 = 2(x + 2).
First you distribute and get 2x+4 = 2x+4.
Subtract 2x from both sides to get 4 = 4, a true statement. So the equation is always true.
For this equation, it should be pretty clear from looking at it.

across · Answer

Simply put,$$x=x$$is an equation that is always true,$$1=2$$is an equation that is always false, and$$x^2=4$$is an equation that is sometimes true.

nory · Answer

Try to solve 3(2x+9) = 6x + 16. What happens?
This equation has no solutions, because the variables cancel and you get 27 = 16, which is false. So this equation is never true.

anonymous · Answer

Great examples, @Nory @across !