Solve the following equation x^2 – x < 0

  • Thread starter tomcenjerrym
  • Start date
In summary, the equation x^2 - x < 0 can be solved by finding the solutions of x^2 - x = 0, which are x = 0 and x = 1. By graphing the function y = x^2 - x, it can be seen that the inequality is satisfied by all values of x between 0 and 1, thus the solution set is {x | 0 < x < 1}. It is important to solve the equation first before determining the solution set for an inequality.
  • #1
tomcenjerrym
37
0
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
 
Mathematics news on Phys.org
  • #2
tomcenjerrym said:
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.
 
  • #3
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}.
 

FAQ: Solve the following equation x^2 – x < 0

What is the first step in solving this equation?

The first step in solving the equation x^2 – x < 0 is to factor the left side.

How do I factor x^2 – x?

To factor x^2 – x, you can use the difference of squares formula, which is a^2 – b^2 = (a + b)(a – b). In this case, a = x and b = 1, so the factored form is (x + 1)(x – 1).

What do I do after factoring?

After factoring, you need to set each factor equal to 0 and solve for x. This will give you the values of x that make the equation true.

What is the final solution to the equation?

The final solution is the set of values for x that make the original equation x^2 – x < 0 true. In this case, the solution is x < 0 or x > 1.

How do I graph the solution to this equation?

To graph the solution, you can create a number line and plot the values of x that make the equation true. In this case, you would plot all numbers less than 0 and greater than 1 on the number line.

Similar threads

Replies
7
Views
1K
Replies
4
Views
1K
Replies
2
Views
1K
Replies
66
Views
5K
Replies
7
Views
1K
Replies
22
Views
1K
Replies
2
Views
1K
Replies
7
Views
1K
Back
Top