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### Solve for X

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Date: 10/09/1999 at 15:52:22
From: Jenna
Subject: I don't understand

Dear Dr. Math,

I'm so confused! I have my math book in front of me and I don't
understand how to do a problem like this:

4x - 1/2 = -3/2

Could you help me and explain it so that I can understand? My book
just confuses me.
```

```
Date: 11/03/1999 at 21:55:22
From: Doctor Sandi
Subject: Re: I don't understand

Hi Jenna,

Don't worry, we'll get to the bottom of it and work it out. Math books
can be pretty confusing because they use math language, which is a
whole new concept in itself that needs to be learned along the way and
makes things seem confusing. I would encourage you to persevere with
your math book though - even though it is confusing, if you keep on
reading it and trying to follow the examples in the book, it will get
easier to understand the more you read it. And, as you get into higher
grades with math, if you can understand a math book, believe me,
you'll do a lot better than you would otherwise.

What I will do, Jenna, is make up an equation similar to yours, and
we'll work through it, find the answer, and then you'll be able to use
the same process to find the answer to your problem on your own. But
before I go on, let me say something about the way you wrote your
question. You need to put brackets around the fractions; otherwise
someone might think it could mean (4x-1)/2 = (-3/2). I'm hoping that
I've guessed right though, and have interpreted your question
correctly.

Let's work through this one:

2x - (1/2) = (-5/2)

We need to find the value of x, so we have to get the 2x on its own.
The first thing to do is to take the -(1/2) over to the other side. Do
you remember that when you take a negative number over to the other
side of an equation, it becomes a positive number? If the number is
negative, to move it to the other side of the equation, the negative
needs to be "undone" and it will then become a positive. So then we
have:

2x = (-5/2) + (1/2)

You could work this out on your calculator, but since they both have
the same denominator (number on the bottom of the fraction) you could
say -5 + 1 = -4, so 2x = -4/2, which cancels down to 2x = -2.

Now let's have a look at the x again. It is nearly on its own but not
quite. We need to get rid of the 2 that is multiplying the x. We need
to move it to the other side and "undo" the multiplying action. What
do we need to do with the 2 when we apply it to the other side to
"undo" the multiplication? Yes, you're right, we'll divide. Then we
have:

x = -2/2
= -1

There, it wasn't really that hard in the end when you worked through
it with me was it? I hope not, anyway. But if it was, take heart
because EVERYTHING is hard to do when we first learn how to do it. So,
my advice to you would be to do as many of these kinds of equations as
you possibly can, and the more you do, the easier it will get, I
promise.

Something that also helps immensely is that now that you have found
the value of x, you could put it back into the original equation to
see if it all checks out. Then you know that you're right (or wrong).
We'll do it with this one:

2x - (1/2) = (-5/2)

So if we write

2(-1)-(1/2) = (-5/2)

we have put the -1 in place of the x and we're hoping that when we
work through it that it does indeed solve to be (-5/2).

Okay, 2 times -1 = -2. -2 - (1/2) = -(5/2). Yes! Now you know that the
answer that we found for x was right, because when we put x = -1 back
into the equation and solve it we get -(5/2) as the answer, just as
it's meant to be. This is good to remember in exams (if you have
time). You can often check your answers by working backward.

Here are some links that you might like to have a look at. You'll see
that they are questions that other people have asked Dr Math together

Algebra
http://mathforum.org/dr.math/tocs/algebra.middle.html

Equations
http://mathforum.org/dr.math/tocs/equation.middle.html

Negative Numbers
http://mathforum.org/dr.math/tocs/negative.middle.html

Word Problems
http://mathforum.org/dr.math/tocs/wordproblem.middle.html

If you click on "Back to Middle School Level" on these pages you'll
see that there are many more topics, and if you click on "Search Dr
Math" you'll be able to search the whole archive for whatever topic
you want.

In the meantime though, if you don't understand how we did the
equation above and you have more questions about this type of thing or
any questions about any other areas of mathematics that you would like
to ask, we'd like to hear from you. Just email us and we'll try to
help.

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

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