# Solving Equations with Fractions: -7x + 3 = -15 / 2

#### mm_b_sm

##### New member
I am having trouble with this problem. Can anyone help me?

-7x + 3 = -15 over 2

I am not sure how to start out answering this question.

#### tkhunny

##### Moderator
Staff member
What's the question? Generally, a problem comes with some sort of instruction.

If you are to solve, there are various ways to go about it.

1) Get rid of the fractions (by learning ho wto deal with them, not by being afraid of them).
2) Don't worry about the fractions, since it is quite possible we'll just get them right back.

Version 1

-7x + 3 = -15/2

Multiply by 2

-14x + 6 = -15

Subtract 6

-14x = -21

Divide by -14

x = -21/(-14) = 21/14 = 3/2

Version 2

Notice, above, that we ended with fractions despite our efforts.

-7x + 3 = -15/2

Subtract 3

-7x = (-15/2) - 3 = (-15/2) - (6/2) = -21/2

Divide by -7

x = (-21/2)/(-7) = (-21)/[(-7)*2] = 3/2

Same result.

#### george22

##### New member
The first solution given to you is the best. Whenver you are dealing with fractions, multiply the WHOLE equation by the denominator. In your case it was 2. When you do that, it eliminates the equation having a fraction even though your answer may still be a fraction.

#### tkhunny

##### Moderator
Staff member
george22 said:
The first solution given to you is the best.
That's just not the case all the time. Sometimes it is best.
Whenver you are dealing with fractions, multiply the WHOLE equation by the denominator.
Maybe. If that appears to be advantageous.

Note to Student: Please don't get ONE method stuck in your head - not for ANYTHING. Keep your mind open. Always look around for simpler, more convenient, more useful, or more understandable results. Never, ever think you are clever if you know only one way to proceed.

Go ahead and learn how to work with fractions. You will be better for it.

#### jonboy

##### Full Member
tkhunny said:
Note to Student: Please don't get ONE method stuck in your head - not for ANYTHING. Keep your mind open. Always look around for simpler, more convenient, more useful, or more understandable results. Never, ever think you are clever if you know only one way to proceed.

Go ahead and learn how to work with fractions. You will be better for it.
YUP TK I so agree w/you. Definetly look for the most efficient way based on the information do not use just use one limited way. A good example is system of equations in my experience and this as well.

#### Denis

##### Senior Member
-7x + 3 = -15 over 2

As TK says...."whatever turns you on" :wink:

Start by changing the signs (no need to, really, but useful in some cases):

7x - 3 = 15 over 2

Code:
 7x - 3      15
--------  = ----
1         2
Now you can do a crisscross multiplication of above:

2(7x - 3) = 1(15)
14x - 6 = 15
14x = 21
x = 21/14 = 3/2

#### tkhunny

##### Moderator
Staff member
...except "crisscross multiplication" It is evil. :evil:

#### Denis

##### Senior Member
tkhunny said:
...except "crisscross multiplication" It is evil. :evil:
...evil even with a single variable to the power 1 :?:
Ya must be a "reborn mathematician" :wink: