# Equations and Inequalities

### Abby Kernion

## One Step Equations

## x + 12 = 32

## Get the variable alone Since there is a positive twelve next to the x we have to subtract twelve from the positive twelve to get x alone and cancel it out. Whatever we do to one side we have to do the same to the other side. 32 - 12 = 20 | ## Rewrite After we have this big mess of numbers we have to clean it up. Once we do this it is much simpler to get the answer. | ## Your Answer! Since we canceled out the only thing stoping us from getting what x equals we have our answer. x = 20! |

## Get the variable alone

Since there is a positive twelve next to the x we have to subtract twelve from the positive twelve to get x alone and cancel it out. Whatever we do to one side we have to do the same to the other side. 32 - 12 = 20

## Rewrite

After we have this big mess of numbers we have to clean it up. Once we do this it is much simpler to get the answer.

## Paint Supplies

Since Audrey stocked up on colored pencils she relized she needs some more painting supplies. She went to the store and bought some paint brushes. She found a pack of paint brushes that she really liked. She bought 8 of those packs. When she got home she emptied the packs. She bought 56 paint brushes. How many paint brushes were in each pack?

## 8x = 56

## Get the variable alone To get the variable alone you have to do the inverse operation. 8x is the same as 8 times x so the inverse of multiplication is division. 8 divided by 8 is 1. 56 divided by 8 is 7. | ## Rewrite Now we basically have 1x = 7, but 1x is the same as x so we rewrite it and it turns into x = 7. | ## Your answer! Now that we rewrote it we have our answer x = 7! All we had to do was use the inverse operation to get the variable alone! |

## Get the variable alone

To get the variable alone you have to do the inverse operation. 8x is the same as 8 times x so the inverse of multiplication is division. 8 divided by 8 is 1. 56 divided by 8 is 7.

## Rewrite

Now we basically have 1x = 7, but 1x is the same as x so we rewrite it and it turns into x = 7.

## One Step Inequalities

## x(9) > 54

## Get the variable alone Since x(9) is multiplication you do the inverse which is division. 9/9 = 1. 54/9 = 6. | ## Rewrite x(1) is also just x so we just put x. Then we have 6 on the other side. | ## Your Answer! Now that we have simplified it we have x > 6! |

## x - 14 < 7

## Get the variable alone Since the 14 next to the x is negative we need to add 14 to cancel it out. And whatever we do her we have to do to the other side. 7 + 14 is 21 | ## Rewrite Now that we got the variable alone and balanced the other side we can make it were we can get the answer easier. | ## Your answer! x < 21 is our answer! That means that Audrey made less than 21 brownies. |

## Get the variable alone

Since the 14 next to the x is negative we need to add 14 to cancel it out. And whatever we do her we have to do to the other side. 7 + 14 is 21

## Rewrite

Now that we got the variable alone and balanced the other side we can make it were we can get the answer easier.