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

a number that is a solution to an equation is the value of a mathematical expression which corresponds to the parameters in question.

eg. y=x^2

when x=2; y=2^2=4

using mathematical language, the expression y=x^2, means that y, the dependent variable, is a function of x, the independent variable, and so using arithmetic one can break down this function into y=x*x .. multiplication can be broken down into simplified counting.

eg. when counting a grid.



one could count each individual row and add them together:

6+6+6+6+6+6+6+6 =48

multiplication is a simplified version of this:

the number six eight times is forty eight.

similarly, exponents are simplified expression for multiplications of the same number..

6^2 .. 6 x 6 = 36