WholeLottaLove wrote:
Is |x| + |x-1| = 1?
For #1 (x≥0) I see two possible cases:
x=1/2
x+ -(x-1)=1
x+ -x+1=1
1=1
OR
x=2
x+x-1=1
2x=2
x=1
Wouldn't that imply that for both cases of x (where we have positive and negative values inside the | | signs) the equation is true?
Thanks!
For #1 (x≥0) I see two possible cases:
x=1/2
x+ -(x-1)=1
x+ -x+1=1
1=1
OR
x=2
x+x-1=1
2x=2
x=1
Wouldn't that imply that for both cases of x (where we have positive and negative values inside the | | signs) the equation is true?
Thanks!
No.
In the first case for an x=\frac{1}{2} (0\leq{x}\leq{1}) you get that the equation is true 1=1 it's like saying ALWAYS TRUE.
But in the second case for an x>1 you get x=1, but since x>1 that is not true
Statement 1 is not sufficient