Question

Solve each absolute value inequality. Graph the solution set. Write the solution in INTERVAL NOTATION.
|x/2-5|+2>10

Answer 1

When working with inequalities, you can add and subtract the same number from each side and preserve the inequality relationship, so for starters, subtract 2 from each side to get the absolute value expression all by itself. What do you get so far? Show work.

Answer 2

|x/2|>13

Answer 3

then do i times by 2?

Answer 4

|x/2|>13 is not correct. On the left side, you have 2 terms: the absolute value term and "2". When adding and subtracting, you deal with only one term, conceptually. Hint: leave the absolute value expression alone for now and just concentrate on the "2".

Answer 5

|x/2-5|>6

Answer 6

You have the left side correct, but the right side is wrong. At this point, I'll give out an intermediate answer, because you are working at it and you are starting to get it, but you're having trouble with adding and subtracting single-digit numbers. 10 - 2 is 8, not 6.

Answer 7

yeah i relized tht after wow

Answer 8

np, we all make mistakes. I make a lot of them, we all do. So now, |a| > m means that for positive a you have a > m and for negative a, you have a < -m. So you will have TWO inequalities because you have to get rid of the absolute value sign so you have to split it up into these 2 inequalities.

Answer 9

ok now i add 5 then tht comes out as |x/2|>13 thts what i typed in earlier

Answer 10

That's not quite it and it only addresses when what is under the absolute value sign is positive., AND most importantly, it will be misleading for doing the other half.

Answer 11

One half of the solution will start with x/2 > 13 , NOT |x/2|>13

Answer 12

but i had 2 get rid of the 5

Answer 13

is it x>169

Answer 14

Yes, you are right, but you first get rid of the absolute value sign or you will mess up your thinking for solving the other inequality. Trust me, you have to go in order with this.

Answer 15

But not right on x > 169

Answer 16

26

Answer 17

I think I better just help you along a little more so here goes.

Answer 18

x/2 - 5 > 8 and x/2 - 5 < -8 No absolute value signs at this point. Goes down to: x/2 > 13 and x/2 < -3. Try it from here. You would never have gotten to the second inequality otherwise if you try to get rid of the -5 first. Have to get rid of the absolute value sign FIRST.

Answer 19

So, 26 is HALF of the answer, but you're on your way. You just have to get the other half now . The OTHER inequality.

Answer 20

x<-14