What does it mean for a number to be the "solution" to an equation?

Give an example of a variable equation and its solution.
Explain in complete sentences how you know that number is the solution.

Question

What does it mean for a number to be the "solution" to an equation?

    Give an example of a variable equation and its solution.
    Explain in complete sentences how you know that number is the solution.

jamesj · Answer

Consider the equation

x + 2 = 5

Saying that "x = 3 is a solution to the equation" means the value of x where x is 3 satisfies that equation, as indeed it does because

3 + 2 = 5.

jamesj · Answer

If you wanted to test whether x = 4 is a solution, you substitute it into the equation and see if the equation is satisfied.

Well, if x = 4, then the equation
x + 2 = 5
says that
4 + 2 = 5

But that is false.  Hence x=4 is not a solution.