SOLUTION: How would I solve this inequality? 4x^2-2x<=0 I tried this 2(x^2-x)<=0 but I don't know what to do next.

Question 137151This question is from textbook College Algebra
: How would I solve this inequality? 4x^2-2x<=0
I tried this 2(x^2-x)<=0 but I don't know what to do next. This question is from textbook College Algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve this inequality? 4x^2-2x<=0
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4x^2-2x <= 0
2x^2-x <= 0
Solve the equality:
2x^2-x = 0
x(2x-1) = 0
x = 0 or x = 1/2
----------------
Draw a number line and mark x=0 and x=1/2 on it.
Take a test value from each of the resulting intervals to see where the
solutions for the inequality are.
Check the test points in x(2x-1) < 0
-------
If x = -10, you get -*- < 0 which is false so no solutions in (-inf,0)
If x = 1/4, you get +*- < 0 which is true so solutions in (0,1/2)
If x =- 10, you get +*+ < 0 whic is false so no solutions in (1/2,+inf)
-----------------------
Final Solution
[0,1/2]
================
Cheers,
Stan H.
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