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### Simple Equation: 3y + 2 over 4 equals 7

```
Date: 10/17/2001 at 17:11:59
From: Tara
Subject: I have some equations I can't seem to understand!

3y + 2 over 4 equals 7

I think you have to subtract 2 on both sides (to get 3y by itself)
3y+2-2 over 4 equals 7-2
3y over 4 equals 5

Now I'm lost! Could you help me out?
```

```
Date: 10/17/2001 at 22:43:11
From: Doctor Peterson
Subject: Re: I have some equations I can't seem to understand!

Hi, Tara.

You have

3y + 2
------ = 7
4

Notice what the left side means: you multiply y by 3, then add 2, then
divide by 4.

When you are undoing these operations, it is necessary to do so in the
reverse order. For comparison, suppose I have put on my shirt, then my
sweater, then my coat. If I try to take off my sweater before taking
off my coat, it will get all tangled up! That's just what happened to
you: the addition of 2 is the sweater, and you took it off too soon.

It is not true that

3y + 2       3y
------ - 2 = --
4          4

which is what you are assuming. Actually, we can simplify the left
side as

3y + 2
------ = 3/4 y + 1/2
4

and then subtract 1/2 rather than 2. But if you don't want to
simplify, just undo the division (by multiplying by 4) before the

3y + 2
------ = 7
4

3y + 2 = 7 * 4

3y + 2 = 28

Now you can subtract 2 from both sides, and so on:

3y = 28 - 2

3y = 26

y = 26/3

Does that help?

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Equations

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