Question

What's wrong with this method?
|x-1|<2x
Either x-1<2x or x-1>-2x
x>-1, x>1/3
So x>-1
But the correct answer is: x>1/3.

Answer 1

hello iaf x = -1

Answer 2

*if
-2 = -2

Answer 3

I don't get what you are trying to say.

Answer 4

@psujono What are you writing? :)

Answer 5

|x-1| < 2x

can be re-writen as two equations with separate DOMAINS

for x - 1 ≥ 0, or x ≥ 1 it is
x - 1 < 2x

for x - 1 < 0, or x < 1 it is
-(x - 1) < 2x
or
x - 1 >- 2x

now solve, but pay attention to the domains

x - 1 < 2x
-1 < x (Domain is x ≥ 1) so that's NOT OK

x - 1 > -2x
3x > 1
x > 1/3 (Domain is x < 1) so that's also ok

So the final answer is x > 1/3

Answer 6

The domain always gets people