Question

How do you know if an equation is always, sometimes, or never true?

Answer 1

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.

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

Simply put,

x=x

is an equation that is always true,

1=2

is an equation that is always false, and

x2=4is an equation that is sometimes true.

Another example: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