Question

solve the inequality Ix^2-xI 14 years ago

Answer 1

you have to solve two inequalities.

Answer 2

\[|x^2-x|=x^2-x\] if x< 0 or x > 1
\[|x^2-x|=x-x^2\] if 0< x < 1

Answer 3

http://www.wolframalpha.com/input/?i=abs%28x^2+-+x+%29+%3Cx - it the best one!)
From it you can see? that the segment (0,2) is the solution.

Answer 4

so if x > 1 you get
\[x^2-x< x\]
\[x^2-2x< 0\]
\[x(x-2)<0\]
the solution there is
\[(0,2)\] but we assumed x > 1, so solution is
\[(1,2)\] then we solve the next inequality.

nikita is right you can graphs with wolram or just ask, assuming of course you don't have to do this on a test

Answer 5

satellite 73 is correct but jst a small correction the thing inside mod is positve when x is also less than -1
anyways it makes no diff in the ans

Answer 6

next inequality would be assumes 0 < x < 1 and solve
\[x-x^2<x\]
\[x^2>0\]
\[x>0\] and therefore your answer is
\[(0,2)\]

Answer 7

sriram is also right, but inside is positive when x < 0 if i am not mistaken.