Question 67391
|(2/5)x +1| = |1-x|
Find the zero values.
(2/5)x+1=0
x=-5/2
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1-x=0
x=1
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Draw a number line and mark two points as -5/2 and 1.
This breaks the number line into three segments.  We
need to look for solutions in each segment, keeping in
mind the definition of absolute value.
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In the segment (-inf,-5/2) you get:
-(2/5x+1)=1-x
(2/5)x+1=x-1
(3/5)x=2
x=10/3
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In the segment (-5/2,1) you get:
(2/5)x+1=1-x
(7/5)x=0
x=0
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In the segment (1,inf) you get:
(2/5)x+1 = x-1
-(3/5)x=-2
(3/5)x=2
x=10/3
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Check these answers:
If x=0, |(2/5)x+1| = 1 = |1-x|
If x=10/3,  |(2/5)x+1] = |4/3+3/3| = 7/3 = |10/3-1|

Cheers,
Stan H.