# Intro to equations

Learn what an equation is and what it means to find the solution of an equation.

# What is an equation?

**An equation is a statement that two expressions are equal.**For example, the expression is equal to the expression (because they both equal ), so we can write the following equation:

Here are two more examples of equations:

Let's make sure we know the difference between an expression and an equation.

# True equations

All of the equations we just looked at were true equations because the expression on the left-hand side was equal to the expression on the right-hand side. Let's make sure we understand what a true equation is.

# Solutions to algebraic equations

All of the equations that we've looked at so far have included only numbers, but most equations include a variable. For example, the equation has a variable in it. Whenever we have an equation like this with a variable, we call it an

*algebraic equation*.For an algebraic equation, our goal is usually to figure out what value of the variable will make a true equation.

For the equation , notice how creates a true equation and creates a false equation.

True equation | False equation |
---|---|

$\begin{aligned} \blueD x +2 &= 6 \\\blueD{4} +2 &\stackrel{\large?}{=} 6\\6 &= 6 \end{aligned}$ | $\begin{aligned} \redD x +2 &= 6\\\redD{3} +2 &\stackrel{\large?}{=} 6\\5 &\neq 6 \end{aligned}$ |

*Notice how we use the symbol $\stackrel{\large?}{=}$ when we're not sure if we have a true equation or a false equation.*

The value of the variable that makes a true equation is called a

**solution to the equation.**Going back to our example, is a solution of because it makes the equation true.