# How to solve simple equations

## Solving simple equations: Just undo everything that's been done!

To solve simple equations, start by thinking about what’s happening to the variable. Consider ???x+5=12???. What’s happening to ???x???? It’s being added by ???5???.

Well what’s the inverse operation of addition? How do you “undo” adding by ???5???? Since the inverse operation of addition is subtraction, you’ll subtract ???5??? from both sides to undo the addition of ???5???.

Solving simple equations is really just undoing everything that’s happening to the variable in order to get the variable by itself. Solve by working backwards from the order of operations (undo all addition/subtraction and then undo multiplication/division). Use inverse operations until the variable is alone and remember to do the same thing to both sides of the equation so that it stays balanced.

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## Undoing and operation that's already been done is called the "inverse operation"

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## Solving a simple equation with one inverse operation

**Example**

Solve for the variable.

???x-3=10???

In this example ???3??? is being subtracted from ???x???, to undo subtraction we need to add ???3??? to both sides of the equation.

???x-3+3=10+3???

???x+0=13???

Remember that ???0??? can be added or subtracted from anything and it won’t change the value. Which means that ???x+0??? really just equals ???x???.

???x+0=13???

???x=13???

Inverse operations undo each other. subtraction un-does addition; multiplication un-does division.

Let’s try another example of solving simple equations.

## This example requires us to perform two inverse operations

**Example**

Solve for the variable.

???3x+5=11???

In this example ???x??? is being multiplied by ???3??? and then being added by ???5???. To solve we work backwards from the order of operations so we need to undo the addition first by subtracting ???5??? from both sides of the equation.

???3x+5-5=11-5???

???3x+0=6???

???3x=6???

Now we need to undo the multiplication of ???3???. Division is the inverse operation of multiplication so we will divide both sides by ???3???.

???\frac{3x}{3}=\frac{6}{3}???

???x=2???