Find the values of x in? # |x-1|-|2x-5|=2x#

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Answer 1 · 2018-07-24T14:05:04

There is only one solution #x=-4#.

There are #2# points to consider

#x-1=0#, #=>#, #x=1#

#2x-5=0#, #=>#, #x=5/2#

There are #3# intervals to consider

#I_1=(-oo,1)#

#I_2=(1,5/2)#

#I_3=(5/2,+oo)#

In the first interval #I_1#

#-x+1+2x-5-2x=0#

#x=-4#

This solution #in I_1#

In the second interval #I_2#

#x-1+2x-5-2x=0#

#x=6#

This solution does not #!inI_2#

In the third interval #I_3#

#x-1-2x+5-2x=0#

#3x=4#

#x=4/3#

This solution does not #!inI_3#

There is only one solution #x=-4#

graph{|x-1|-|2x-5|-2x [-18.02, 18.02, -9.01, 9.02]}