## GiggleSquid 2 years ago What is the solution set or set notation for |7x+21|<-7

1. lgbasallote

hint: solve for x in 7x + 21 < -7 AND 7x + 21 > 7 does that help?

2. ParthKohli

Wait, what? An absolute value inequality doesn't have a negative on its right-hand-side!

3. ParthKohli

This is a false statement, and does not satisfy for all $$x$$.

4. ParthKohli

How can an absolute value be less than -7 when absolute value of anything is a positive number?

5. sauravshakya

Do u know the defination of modulas?

6. sauravshakya

IF not then PLZ LOOK AT THIS: let x be any real number. Then the absolute value of x, denoted by IxI, is a non negative real number defined by |dw:1343557688022:dw|

7. ParthKohli

Nope. $$|-x| =x \qquad |x| = x$$

8. sauravshakya

so, when 7x+21>= 0 then 7x + 21 < -7 x<-4 AND when 7x+21<0 then -(7x+21)<-7 x >-2

9. ParthKohli

Oh yes.

10. bhaweshwebmaster

@sauravshakya now subsitute your answer in the question.. does it seem to satisfy? I already posted this solution.. however @ParthKohli forced me (using logic) to delete it.

11. sauravshakya

YA IT SATISFIES @bhaweshwebmaster

12. bhaweshwebmaster

teach me how.. I don't see it..

13. sauravshakya

OH. sorry @bhaweshwebmaster actually there is no solution.... since I 7x+ 21 I >=0