Negative fractions

[Iceycold12]

Hello, I have my Final Algebra I Exam tomorrow (finally!) and I have a small question. Say we have:

solve for x.

I. Add 3 to both sides to cancel -3.
II. We then have

III. Now here's where I must of forgot some basic Algebra, I usually don't multiply by the reciprocal to get rid of 4, I like to multiply by the denominator (works the same way) but does the - in the fraction apply to 4 as well, so are we multiplying 12 by -4 or 4?
IV. The following and final step is to divide -3 by both sides to find x.

Thanks a lot.

 

[wjm11]

Hello, I have my Final Algebra I Exam tomorrow (finally!) and I have a small question. Say we have:

solve for x.

I. Add 3 to both sides to cancel -3.
II. We then have

III. Now here's where I must of forgot some basic Algebra, I usually don't multiply by the reciprocal to get rid of 4, I like to multiply by the denominator (works the same way) but does the - in the fraction apply to 4 as well, so are we multiplying 12 by -4 or 4?
IV. The following and final step is to divide -3 by both sides to find x.

You could multiply by either -4 or 4 as your step III, but the following step depends on that choice. Example:

(-4)(-3/4)x = (-4)12
3x = -48
x = -16

OR

(4)(-3/4)x = (4)(12)
-3x = 48
x = -16

The "-" (negative sign) is not attached to either the numerator or denominator in particular. You could attach it to either one (but not both) and go from there. Alternatively, you could simply think of the negative sign as a (-1):

-(3/4)x = (-1)(3/4)x

Regardless, if you find the negative in front of the fraction confusing, just multiply both sides of the equation by (-1) before you deal with the fraction:

(-1)(-3/4)x = (-1)(12)
(3/4)x = -12
x = -16

Hope that helps.

 

[Iceycold12]

(-4)(-3/4)x = (-4)12
3x = -48
x = -16

So if I understood right, since the "-" sign isn't attached to the numerator nor the denominator once I used it once, say I multiply by -4, the 3x (the numerator) that remains must be positive since I already "attached the negative to the 4 and took it away to the other side to multiply by -4"? A rough understanding, but hopefully it gets the message across.

edit: Didn't see your message Denis but I see, that's much more helpful, now I just want to clear my doubts on the negative version without multiplying by -1. See above ^^^.