|2x/3 + 5| ≥ 6

I cant figure out how to solve this one...I tried (im not sure if it's correct) andi couldnt finish it off.

Thankssss in advance :-)

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- Sep 17th 2006, 05:01 AMCherryHow to solve |2x/3 + 5| ≥ 6 ??
|2x/3 + 5| ≥ 6

I cant figure out how to solve this one...I tried (im not sure if it's correct) andi couldnt finish it off.

Thankssss in advance :-) - Sep 17th 2006, 05:08 AMQuick
when you have an absolute value inequality you have to realize that |-6|=6

so that when you have an inequality like**|x-2|>3**you can solve by rewriting it to be:**x-2>3 and/or x-2<-3**thus x would be**x>5 and/or x<1**

now you try solving your inequality and show us the work. - Sep 17th 2006, 05:24 AMThePerfectHacker
- Sep 17th 2006, 05:33 AMCherry
okay thanks guys..

here i tried to solve it...i hope its correct...

|2x/3 + 5| ≥ 6

2x + 15 divided by 3 ≥ 6

2x + 5 ≥ 6

2x ≥ 6 - 5

x ≥ 1/2

or

|2x/3 + 5| ≥ -6

= x ≥ -11/2

:confused: gosh...why do i feel like its wrong?? anyhow please let me know if its correct or wrong thanks! - Sep 17th 2006, 05:38 AMThePerfectHacker
- Sep 17th 2006, 06:00 AMCherry
Oh oh how stupid of me..I cancelled out the sum!!

so..

|2x+15| ≥ 18

2x ≥ 18 - 15

2x ≥3

x ≥ 3/2

it's correct, right?

Thanks ThePerfectHacker. I didnt pay attention to the fact that 3 is divided by 2x + 15 not only 15. - Sep 17th 2006, 06:18 AMThePerfectHacker
- Sep 17th 2006, 06:38 AMCherry
Yeah I know, I figured out how to do the other one :) and yep you're right I better add the signs.

Thanks again, and thanks to Quick. You guys are so much better than my teacher who perfers to ignore than help out pfft. You guys rock :D - Sep 17th 2006, 07:55 AMQuick
- Sep 17th 2006, 11:41 AMThePerfectHacker
It is a question that tests your understanding of math. I dare you to ask it to your stupid physics teacher no way she can get it.

Did you try graphing them?

y=abs(x) and y=abx(x+1) and see where they interesect.

---

The solution to that equation (and this is why I like it so much besides for it being my problem) is that,

-1<=x<=0

There are infinitely many solutions! - Sep 17th 2006, 12:59 PMQuick
- Sep 17th 2006, 02:09 PMThePerfectHacker
I actually meant to say,

|x|+|x+1|=1 - Sep 18th 2006, 02:29 AMTD!
As a reference, ThePerfectHacker posted this problem here, where you can also find a solution.

- Jul 12th 2007, 11:38 AMTHE pdTHE pd
- Nov 10th 2007, 07:11 AMqspeechc
|2x/3+5| ≥ 6

I think it is important to remember:

|x| = x if x ≥ o

and

|x| = -x if x ≤ 0

So:

If 2x/3 + 5 ≥ 0, then:

2x/3+ 5 ≥ 6

And solve:

x ≥ 3/2

Now, if 2x/3 + 5 ≤ 0, then:

-(2x/3 + 5) ≥ 6

2x/3 + 5 ≤ -6

2x/3 ≤ -11

x ≤ -33/2