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 
addition:

    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/