## Calcmathlete 3 years ago Find the solution set of the inequality: |2x + 5| + |4x + 7| < 30 How would you do this kind of problem? I'm not familiar with how to do it when there are two separate absolute values...

1. sai1234

u can write |2x + 5| as2x + 5 or -(2x + 5) like that |4x + 7| as(4x + 7) or -(4x + 7) so totally there as 4 possibilities

2. Calcmathlete

Alright. I'm still a bit confused...would I do them all separately?

3. experimentX

plugin into wolfram ... something interesting there

4. Calcmathlete

lol...it is a bit interesting...I need to know how to do these without wolfram though...

5. experimentX
6. Calcmathlete

Is that really what I do?

7. experimentX

i'm not sure .... though this technique seems pretty promising

8. Calcmathlete

But all that results in is the removal of the absolute value no?

9. experimentX

yep ... take square and see |dw:1344019775207:dw|

10. Calcmathlete

I am so confused...not going to lie...if you take the square of both sides, wouldn't you end up with the second side: |dw:1344019964409:dw| and where did the absolute value come back in?

11. experimentX

sorry .. my bad

12. experimentX

|dw:1344020042743:dw|

13. experimentX

looks like this is going to be quite difficult ...

14. Calcmathlete

Yeah...my teacher said that there was a very simple trick to this, but she never had the opportunity to teach it to me, so I'm just stuck on what to do...

15. experimentX

|dw:1344020241753:dw|

16. experimentX

for x is positive.

17. Calcmathlete

Well, turns out that sai at the beginning was correct...you just work out the 4 different cases...

18. Calcmathlete

I found the solution set...

19. Calcmathlete

Thanks for trying though...

20. experimentX

for x is negative, |dw:1344020308613:dw|

21. experimentX

check the value for a = 3, which is less than 30|dw:1344020674321:dw|

22. experimentX

|dw:1344020722686:dw|

23. experimentX

|dw:1344020797357:dw|

24. Calcmathlete

Yup. I get it now. We just test out all 4 possibilities and combine the inequalities. Thank you :)

25. experimentX

well ... the best would be do see carefully how it takes the least effort ...

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