Help with inequalities

[twilightrose]

I am homeschooled, and my mom and I have been studying a particular problem for a while now and don't understand the answer at all.
The problem is: -1/2(x-10)>7
-1/2x+5>7
-1/2x+5-5>7-5
-1/2x>2
-2(-1/2x)<-2(2)
x<-4
We have no idea where the 5 came from in the second line, or where the negative in front of the 2 came from in line 5. We are completly stumped. According to our text book this is exactly how it should be done, and is the answer. We are stuck.

 

[pka]

\(\displaystyle \L
\left( {\frac{{ - 1}}{2}} \right)\left( { - 10} \right) = 5\)

 

[twilightrose]

Binary numbers? What? I don't understand them then. Oh, that's your sig. Math is not my subject.
How did you get what you just wrote?

 

[pka]

\(\displaystyle \L
\left( {\frac{{ - 1}}{2}} \right)\left( {x - 10} \right) = \left( {\frac{{ - 1}}{2}} \right)x + \left( {\frac{{ - 1}}{2}} \right)( - 10) = \left( {\frac{{ - 1}}{2}} \right)x + 5\)

 

[twilightrose]

Oh! :idea: I get that. Thanks! I still don't get the -2, though.

 

[pka]

\(\displaystyle \L
\left( {\frac{{ - 1}}{2}} \right)x > 2\quad \Rightarrow \quad - x > 4\)

But we don’t want −x but +x.
So \(\displaystyle \L
x < - 4\)

 

[twilightrose]

Oh! Thank you so very much I really appreciate it!