Equations are mathematical statements that say that two (2) expressions are equal. Expressions are mathematical phrases that may contain a combination of variables, numbers, or operations.

Let’s begin with the definition of what a variable is. Variables are symbols (usually letters) that stand for values that may vary. What follows next is the definition of equations.

Equations are mathematical statements that equate two (2) mathematical expressions. The main difference between mathematical expressions and equations is the presence of the “equals” sign.

For example:

Both x + 2y + 3 and x + 2x – 3 are mathematical expressions, while x + 3 = 4 and x = 9 are equations.

Next, we’ll look at the definition of what the solution of an equation is, what it means to be a Solution.

Solutions of equations are numerical values that satisfy the equation. This when variables in the equations are replaced by the solution like true statement results.

Here is our example number one: Show that the number 3 is a solution to our equation x + 8 = 11.

The solution is: substitute 3 for x in our equation and then simplify.

x + 8 = 11

3 + 8 = 11

Since both the left and the right sides of the last line are equal, it demonstrates that when the number 3 is substituted for x in our equation, a true statement results.

Therefore, the number 3 is a solution to our equation.

Now, example number two: Is 23 a solution of equation 4 = y − 11?

4 = y − 11

Substitute 23 for y.

4 = 23 − 11

4 = 12

Because the left and the right sides of this last line are not equal, this demonstrates that when 23 is substituted for y in our equation, a false statement results. Therefore, the number 23 is not a solution to our equation.

Next Lesson: Equivalent Equations

*Last Updated on April 12, 2021.*