## kenneyfamily 2 years ago solve the inequality (-2/3) | x+5 | < 12 a. x >7 or x<-7 b. x>7 or x< -17 c. -17<x<7

1. Hero

Hint: Multiply both sides by -3/2

2. kenneyfamily

|x+5| < -18 @Hero ??

if when multiply by a negative number ur equation sign must reverse be >

4. Hero

If one side represents distance and the other side has a negative number, can distance be negative?

5. kenneyfamily

i thought that was only for division?

division still family with multiply :p

7. Hero

Bro, if you multiply or divide by a negative number, it doesn't matter. You have to switch signs.

8. Hero

|x+5| > -18 Now that gives us a valid equation to work with since distance (being positive) can be greater than a negative number.

9. kenneyfamily

ok so | x+5 | > -18. now you subtract 5 right? so thats x > -23. thats not a choice

10. Hero

Bro, the five is trapped inside the absolute value symbol. What will you do to "free" it?

11. kenneyfamily

i dont know

12. Hero

18 > x + 5 > -18 x + 5 < 18 x + 5 > -18

13. Hero

x < 18 - 5 x > -18 - 5

14. kenneyfamily

x<13 and x>-23

15. kenneyfamily

but how does that help? its not a choice

16. kenneyfamily

@Hero ? sorry to bother you

the question is wrong :p

18. kenneyfamily

great....so my best guess? maybe c? @RadEn

yes, like u said before the solution should be x<13 or x>-23 (dont use word "and")

or similar by : -23 < x < 13

21. Hero

I think the solution is all real numbers

22. Hero

I double-checked on my calculator and on wolframalpha

yea, all real number :) - multiply by abs number always be negative, right ? because abs number must be positive

24. Hero

Yeah, this is the type where you cannot solve for x by using normal algebra methods. You just have to look at it and realize distance will always be greater than a negative number

25. Hero

@kennyfamily, double check and make sure you posted the question correctly.