Question 1087726
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<pre>
{{{2x^2}}} <= {{{5x - 2}}}.

Move the terms from the right side to the left, changing the signs. You will get an equivalent inequality

{{{2x^2 - 5x + 2}}} <= 0.

Factor the left side:

(2x-1)*(x-2) <= 0.


Divide both sides by 2. You will get an equivalent inequality

(x-1/2)*(x-2) <= 0.     (1)


1)  If  x < {{{1/2}}}  then both factors (each factor) in the left side of (1) are/is negative,
    So the product is positive.


2)  If  {{{1/2}}} < x < 2  then the factor (x-1/2) is positive, while the factor (x-2) in the left side of (1) is negative,
    so the product is negative.


3)  If 2 < x  then both factors (each factor) in the left side of (1) are/is positive,
    so the product is positive.


<U>Answer</U>.  The given inequality has  the segment  [1/2,2] as the solution set.
</pre>

Solved.



If you want to learn on how to solve quadratic inequalities, read the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Inequalities/Solving-problems-on-quadratic-inequalities.lesson>Solving problems on quadratic inequalities</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Inequalities</U>".