abs(7x-6)<43-2x<abs(3-2x)

Question

the equaiton has to absolute value inequalities with an equaiton in the middle.  I did try the different possibilites but what is my final answer.  I worked out when the first is pos and the second is neg and vic versa, i even did it when the two absolute values are neg.  but what is my final answer

Answer 1

Your final answer is "no solution".

I am serious, I checked it up and there is no solution to this inequality.

Answer 2

Thanks a whole bunch, now i can move on to the next wierd question.

Answer 3

abs(7x - 6) < 43 - 2x

do 7x - 6 < 43 - 2x and 7x - 6 > -43 + 2x

9x < 49 and 5x > -37

then x<49/9 and x>-37/5

 

part 2: 43 - 2x < 3 - 2x and 43 - 2x > -3 + 2x

43 - 2x < 3 - 2x is a false statement as 43 is not < 3

then 43 - 4x > -3

-4x> -47

x<47/4

when you test multiple areas less than and greater than these numbers, it does not appear that anything works.

therefore I believe the answer is no solution