# simplify by multiplying by -1 ( Solving equations in terms of a variable)

I am trying to learn Algebra. I'm using Khan Academy, and I just "solved" this problem.

I understand all the steps, except #4.

Could someone please tell me why I would multiply by -1 to simplify the solution?

Solve for u.

uv−5uw−4u+9=8v−9

1. Combine constant terms on the right.

uv−5uw−4u+9=8v−9

uv−5uw−4u=8v−18

2. Factor out the u.

u⋅(v−5w−4)=8v−18

3. Isolate the u.

u=8v−18 / v−5w−4

4. We can simplify this by multiplying the top and bottom by −1.

u= 8v+18 / −v+5w+4

-
In addition to Robert's answer, your step 4 yields an incorrect result. It should be $$u=\frac{-8v+18}{-v+5w+4},$$ instead. – Cameron Buie Jan 2 '13 at 7:42
Cameron, your formatting of Math looks great. Could you tell me how to do that, or point me in the right direction? – I-Ii Jan 2 '13 at 8:02
@Jason: take a look here. – Fabian Jan 2 '13 at 8:29
@Fabian, thank you. – I-Ii Jan 2 '13 at 8:32

The last step, as reported, is incorrect. If we multiply top and bottom by $-1$, we should get $18-8v$ on top. Or the less attractive and potentially confusing $-8v+18$.