SOLUTION: I'm having some trouble with this problem: Solve the inequality x^2 less than or equal to 2x and write the solution set in interval notation.

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Question 1038928: I'm having some trouble with this problem:
Solve the inequality x^2 less than or equal to 2x and write the solution set in interval notation.
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A. (�infinity, 0] U [2,infinity)
B. [0, 2]
C. (�infinity, 2]
D. (�infinity, 2] U [0, infinity)
any help will be greatly appreciated, thank you!

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
selection B.

here's why:

start with x^2 <= 2x

subtract 2x from both sides of the equation to get x^2 -2x <= 0

solve for x^2 - 2x = 0 to get x = 0 or x = 2.

analyze the function when x < 0 and when x > 2 and when x between 0 and 2.

you will find that the function is positive when x < 0 and when x > 2 and that the function is negative when x is between 0 and 2.

therefore x have to be greater than or equal to 0 and less than or equal to 2.

in interval notation, that would be [0,2].

you can graph the function of x^2 - 2x = y and you will see that the graph is positive when x < 0 and that the graph is positive when x > 2 and that the graph is less than or equal to 0 when x is greater than or equal to 0 and less than or equal to 2.

here's the graph.