How do you graph and solve #|x-5|+|2-2x|=7 #?

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Answer 1 · 2016-06-30T23:32:07

#x = {0,4}#

#abs(x-5)=7-2abs(x-1)# gives

1) #x-5=7-2abs(x-1)#
#->x-12=2abs(x-1)#

1-a) #x-12=2(x-1)#
#->-12=x-2#
#->x=10#

1-b) #x-12=-2(x-1)#
#->3x=12+2#
#->x=14/3#

2) #-(x-5)=7-2abs(x-1)#
#->-x-2=-2abs(x-1)#
#->x+2=2abs(x-1)#

2-a) #x+2=2(x-1)#
#->2=x-2#
#->x=4#

2-b) #x+2=-2(x-1)#
#->3x+2=2#
#->x=0#

Checking the solutions

#x = {-14/3,0,4,10}#

we keep the very solutions: #x = {0,4}#