*Last Updated on September 11, 2024.*

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

**Next Lesson:**Equivalent Equations

### Video Transcription

Equations are mathematical statements that equate two (2) mathematical expressions. It’s quite simple: the main difference between mathematical expressions and equations is whether there’s an “equals” sign or not.

For example:

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

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

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Solutions of equations are numerical values that satisfy the equation. This is when variables in the equations are replaced by our solutions, true statements result.

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 side and the right side of this last line are equal, it demonstrates that when we substitute x for the number 3 in our equation, the result is a true statement.

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 side and the right side of this last line are not equal, this demonstrates that when we substitute y for 23 in our equation, the result is a false statement. Therefore, the number 23 is not a solution to our equation.