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.

Answer 1

Basically, in order for a number to be the "solution" to an equation, the equation can only be true if the variable is equal to that number. If you were to substitute a different number for the variable in the equation, then the two sides of the equation would not be equal.

If you were given the equation:

2(x + 7) = 18

then the only way on earth for the two sides for the equation to be equal (the left side equals the right side) is if the variable "x" were 2. If you were to substitute 2 for x, then the equation would be true, and if you were to substitute any other number, the equation would be false.
So 2 is the ONLY number that could replace "x" and keep the equation true, therefore 2 is the solution to this equation.

Sometime more than one number could be solutions to an equation (so there doesn't always have to be only one solution).

Answer 2

am i right ? @ajprincess

Answer 3

solutions don't have to be unique

Answer 4

a number is a solution if you plug your number into your equation and the right hand side equals the left hand side

Answer 5

so for example in the equation \(x^2=1\)

1 is a solution since \(1^2=1\)

and -1 is a solution since \((-1)^2=1\)