How do you solve #3| x - 5| + 2> 9x + 14#?

1 Answer
Jan 19, 2018

See below.

Explanation:

#3| x - 5| + 2 > 9x + 14 rArr 3abs(x-5) > 9x+12 = 9(x-5)+57#

now following with

# 3abs(x-5) > 9(x-5)+57# assuming #x ne 5#

#1 > 3(x-5)/abs(x-5)+57/(3abs(x-5))# or

#1 > pm 3 + 57/(3abs(x-5))# or

#4 > 57/(3abs(x-5))# (the option #-2 > 57/(3abs(x-5))# is not feasible)

so

#abs(x-5) > 57/12# or

#5-57/12 < x < 5 + 57/12#