How do you solve #-3| x + 5| - 1= 9x - 7#?

1 Answer
MeneerNask
Oct 27, 2016

With absolutes, you actually have two equations to solve:

Explanation:

(1)
#x>=-5->x+5>=0# so the absolute bars may be removed:
#-3(x+5)-1=9x-7->#
#-3x-15-1=9x-7->-12x=9->#
#x=9/(-12)=-3/4#
This a valid solution as it also complies with the starting condition that #x>=-5#

(2)
#x<-5->x+5<0# so we have to flip the signs:
#-3(-x-5)-1=9x-7->#
#3x+15-1=9x-7->-6x=-21->#
#x=(-21)/(-6)=7/3#
And this is not a valid solution, as the condition at the start of (2) was that #x<-5#

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