Inequality word problem

[daremkd]

I'm going through Khan academy (to be precise, this video http://www.youtube.com/watch?v=RHe9X2HDEjA) and can't understand the 3:00 part where he says that

for |w-150| <= 2.5

w-150 <= 2.5 and ALSO w-150 >= - 2.5

Why does w-150 >= -2.5? I know the signs change when you multiply/divide by a negative number but here you do it just on the right side, wouldn't it be:

-w+150 >= -2.5. Isn't this right (to do is on the both sides)?

Thank you.

 

[srmichael]

I'm going through Khan academy (to be precise, this video http://www.youtube.com/watch?v=RHe9X2HDEjA) and can't understand the 3:00 part where he says that

for |w-150| <= 2.5

w-150 <= 2.5 and ALSO w-150 >= - 2.5

Why does w-150 >= -2.5? I know the signs change when you multiply/divide by a negative number but here you do it just on the right side, wouldn't it be:

-w+150 >= -2.5. Isn't this right (to do is on the both sides)?

Thank you.

Not quite.

It would be -(w-150) <= 2.5 or, equivalently, w-150 >= -2.5 if you divide both sides by the negative.