Question

What is the Solution set for |2x-8|>or=10

Answer 1

This is for inequalities where you have a "greater than" and absolute value, so you will have 2 closed rays because you are looking for the "distance away".

Answer 2

I dont get it how would u work it out?

Answer 3

So, break the problem up into the positive and the negative areas on the number line. The positive will give you x >= 9, because you are looking for where 2x - 8 >= 10. This is just from solving for x. Once you understand this, we'll get to the negative part.

Answer 4

okay so what i have now is 2x-8>=10??

Answer 5

When working with absolute value and you are just starting out with attacking these problems, conceptually you have to start at the beginning, so |2x - 8| will be positive always because the whole thing is between the absolute value signs. However, 2x - 8 itself, (without the absolute value signs) can be positive or negative. That's really the starting point, realizing this.

Answer 6

okay when do i drop thge absolute value bars?

Answer 7

So, you have TWO problems really and actually. The first problem is what is 2x - 8 >= 10 for when 2x - 8 is >= 0 and the second problem is what is 2x - 8 <= -10 for when 2x - 8 is <= 0.

Answer 8

one negitive and ones positive

Answer 9

For the last question, x <= -1. So you have the 2 answers together. Yes, 2 areas for x. The negatives and the positives.

Answer 10

And x >= 9.

Answer 11

2x-8>=10 and 2x-8<=-10

x<=-1 and x>=9

Answer 12

That's it!

Answer 13

Awesome! a few more of those and i'd probably get it!

Answer 14

They do take a little practice. But more important is the concept of "distance away" in either direction.

Answer 15

okay thanks for the tip (: