How do you solve #|x+5| = 2x+3# and find any extraneous solutions?

1 Answer
Jun 22, 2016

Answer:

#x = 2#

Explanation:

#|x+5| = 2x+3 = x+5 +x-2#

#1=(x+5)/abs(x+5)+(x-2)/abs(x+5)#

but for #x ne -5->(x+5)/abs(x+5) = pm1#

#1 pm 1 =(x-2)/abs(x+5)# we have two possibilities

#1)# #0 = (x-2)/abs(x+5)->x = 2#
#2)# #2 = (x-2)/abs(x+5)->x = O/#
because for #x>2->(x-2)/abs(x+5) < 1#