− 1 ≤ | − 8 x + 7 | --------- − 4 | x + 5 | < − 9

Answer 1

Hi,

− 1 ≤ | − 8 x + 7 | --------- − 4 | x + 5 | < − 9

Beautiful note!

− 1 ≤ | − 8 x + 7 | is always true because always absolute value is positive, so greater than -1 will be true too.

Now:− 4 | x + 5 | < − 9 both side divided by -4 ( switch sign)

| x + 5 | > 9/4

I am sure you know this property: | x | > k ---> x > k , x < -k

after compare this property with inequality we have: x + 5 > 9/4 , x + 5 < -9/4 now solve it is easy

x> 9/4 -5 , x < -9/4 - 5

x > -11/4 , x< -29/4

I hope it is useful.

Minoo