Inequality

[tomcenjerrym]

Does anyone can solve the following equation

x^2 – x < 0

Here is the solutions of mine:

x^2 – x < 0
x(x – 1) < 0
x < 0, x < 1

Please advance

[CRGreathouse]

x^2 – x < 0
x(x – 1) < 0
x < 0, x < 1

To get from line 2 to line 3, you're acting like this is an equality -- it's not. Try graphing y = x^2 - x and you'll see the answer directly -- then factoring like you did will help you get the exact answer.

[HallsofIvy]

Best way to handle general inequalities: solve the equation first:
To solve x2- x< 0, solve x2- x= x(x- 1)= 0. The solutions are, of course, x=0 and x= 1. Since f(x)= x2- x is continuous (all polynomials are continuous), those are the only places where the function can change sign. If x= -1 (-1< 0), (-1)2- (-1)= 2> 0. That tells us that all values of x less than 0 make x2- x positive. That does not satisfy the inequality so no value of x< 0 can. Take x= 1/2 (between 0 and 1). (1/2)2- (1/2)= 1/4- 1/2= -1/4< 0. That tells us that all values of x between 0 and 1 make x2- x negative. That satifies the inequality. Finally, take x= 2 (2> 1). 22- 2= 4-2= 2> 0. That tells us that all values of x larger than 1 make x2- x positive. That does not satisfy the inequality so no value of x larger than 1 does. The solution set for x2- x= 0 is {x| 0< x< 1}.