SOLUTION: 2/5x +1 = 1-x On both sides of the equal sign are absolute value brackets. What I'm unsure of is, what or how do I get rid of the fraction 2/5x ? Thanks, Bob

Question 67391This question is from textbook
: 2/5x +1 = 1-x
On both sides of the equal sign are absolute value brackets. What I'm unsure of is, what or how do I get rid of the fraction 2/5x ?
Thanks,
Bob This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
|(2/5)x +1| = |1-x|
Find the zero values.
(2/5)x+1=0
x=-5/2
----------
1-x=0
x=1
------------
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.
------------------------------------
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
-------------
In the segment (-5/2,1) you get:
(2/5)x+1=1-x
(7/5)x=0
x=0
-------------
In the segment (1,inf) you get:
(2/5)x+1 = x-1
-(3/5)x=-2
(3/5)x=2
x=10/3
-------------
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.
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