Question

|x+1|>|x-1|

Answer 1

Try a few positive values for x and see if the inequality is true. x = 1, 2, 3, etc.
Then try x = 0 and see if the inequality is true.
Try a few negative values for x and see if the inequality is true. x = -1, -2, -3, etc.

Then you will know for what values of x the inequality is true and that will be your answer.

Answer 2

\[1-x >\left| x+1 \right|> x-1\rightarrow take : \left| x+1 \right|>x-1\rightarrow \rightarrow x\]

Answer 3

\[x<0<4\]

Answer 4

take
\[1-x>\left| x+1 \right|\rightarrow x+1>1-x \rightarrow x>0\]

Answer 5

I make amistack in first case x<0<1