Soliving inequalities mathematics?

Question

2x^2-x>=0 i factored out x so x(2x-1)>=0 than solved separately x>=0

and 2x-1>=0 ..so that's x>=(1/2) but in the back of the book answer is

x<=0 and x>=(1/2) what did i do wrong

Answer 1

x(2x-1)&gt;=0

means both are positive or both are -ve or one is zero

x &gt;0 &amp;2x-1&gt;0=&gt; x &gt; 0 and x&gt;1/2 so x &gt;1/2

x &lt;0 &amp; 2x-1 &lt; 0=&gt; x &lt;0 and x &lt; 1/2 so x &lt; 0

x = 0 or 1/2 makes x(2x-1) = 0

so x &lt;= 0 or x&gt;= 1/2

if product of 2 numbers is positive then both are positive or both are -ve.

you missed the 2nd aprt.

Answer 2

You have the right idea, but when you separate the two quantities and separate them to find the answer, you aren&#039;t looking for the answer itself.  You&#039;re finding the critical values 0 and 1/2.  

You need to put 0 and 1/2 on a number line.  Now, choose numbers to plug back into the inequality (use the one you solved out with the two quantities x(2x - 1) ≥ 0.  what I will explain will be easier to do it with this).  Now, choose a number less than 0, in between 0 and 1/2, and greater than 1/2.  These are the intervals you are looking at for your answer.

Plug those numbers into x(2x - 1) and determine whether the answer will be negative or positive.   Write that down on the sign chart.  This tells you whether each interval is negative or positive.  The intervals&#039; sign needs to be positive, so therefore your answer is x ≤ 0 and x ≥ 1/2.

I hope this all makes sense.