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### Course: Algebra (all content) > Unit 2

Lesson 1: Algebraic equations basics# 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

All equations have an equal sign ($=$ ). The $=$ sign is $+$ ) or subtraction ($-$ ) symbols. The equal sign doesn't tell us what to

*not*an operator like addition (*do*. It only tells us that two expressions*are*equal. For example, in:The $-$ sign tells us what to do with $6$ and $2$ : subtract $2$ from $6$ . However, the $=$ sign does $6-2$ and $3+1$ . It only tells us that they

*not*tell us what to*do*with*are equal*.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 $=$ , but the two expressions are

**true equations**because the expression on the left-hand side was equal to the expression on the right-hand side. A**false equation**has an*not*equal to each other. For example, the following is a false equation.When we see an equation that's not true, we can use the not equal sign ($\ne $ ) to show that the two expressions are not equal:

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 $x+2=6$ 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 $x+2=6$ , notice how ${x=4}$ creates a true equation and ${x=3}$ creates a false equation.

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

*Notice how we use the symbol*$\stackrel{?}{=}$ 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 $x={4}$ is a solution of $x+2=6$ because it makes the equation true.

**solution to the equation.**Going back to our example,## Let's try a few problems

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