SOLUTION: for what values of c does |2x+1|= x+c have two solutions? Thanks

Question 825006: for what values of c does |2x+1|= x+c have two solutions?
Thanks
Found 2 solutions by josgarithmetic, tommyt3rd:
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
2x+1>0:
2x+1=x+c
'
2x+1<0:
-2x-1=x+c

Use the two resulting equations.
2x+1-x=c and -2x-1-x=c
x+1=c and -3x-1=c
Giving

That means: and

The equation would have just one value for c.

What if you would try solving for c first instead of x?
x+1=c and -3x-1=c
x=c-1 and -3x=c+1
x=c-1 and x=(c+1)/(-3)
then
c-1=-(c+1)/3
3c-3=-c-1
4c=-1+3
4c=2
, just like before.
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
Solving this problem by analyzing the graphs is the easiest way I can think of...
y=|2x+1|
y=x+c
these two graphs will not intersect for any value of c < 1/2 and at c=1/2 there is only 1 intersection. So we can see that the graphs will intersect at exactly two points for any value of c > 1/2

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