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anonymous
 5 years ago
how to solve x from x/2000 < 100x/(100x+1600)??
anonymous
 5 years ago
how to solve x from x/2000 < 100x/(100x+1600)??

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Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2these questions are more sensitive than we all think, so let's go through it carefully

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2remember that when we multiply negative numbers in inequalities the < has to switch into > ?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2since you have a denominator that has a variable on the right side, (100x+1600) we are not really allowed to multiply it on both sides and cancel it because we don't know if the number is negative or positive, so this is the step that you have to take

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i forgot to mention it. x is nonnegative.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2\[{x \over 2000 } < {100x \over 100x+1600}\] \[x < {200000x \over 100x + 1600}\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2so far I multiplied positive numbers so it is ok, now what you have to do is to gather all expressions on one side and make it into one big fraction as follows

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2\[x {200000x \over 100x+1600} < 0\] \[{x(100x+1600) \over 100x + 1600} {200000x \over 100x + 1600}\] <0

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2\[{100x^x+1600x  200000x \over 100x+1600} <0\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2\[{100x^2  198400x \over 100x+1600} < 0\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2lets factor out the 100s (I should have done this first to make the calculations look better :\ ) \[ {x^2  984x \over x + 16} <0\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2now we are ready to solve this

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2the numerator factors into x (x1984) and the denominator is x+16

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2this is what you are going to do check the intervals between the x's that makes the numerator = 0 and the denominator = 0

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2we can easily see that the numerator = 0 when x=0 or x = 1984 and the denominator =0 when x = 16 so the interval we check is (16)(0)(1984) the left of 6, between 16 and 0, between 0 and 1984 and after 1984

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2the idea is this , all we need to do is to check whether \[x(x1984) \over x+16\] becomes negative or not, so we will plug in numbers that falls into the above interval and check for the sign

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2for example less than 16 we can plug in 100 to see the sign of each factors it becomes \[()() \over()\] which is negative

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2so one part of the solution is x < 16

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2now we check the rest I will let you try doing the other parts, but between 0 and 1984 we can confirm that the rational expression will become negative and the rest positive as such if we plugged in x=1 into the rational expression, we get \[(+)() \over (+)\] which is negative

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2thus the full answer would be x < 16 or 0<x<1984

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2lets' summarize 1), gather all rational expressions on one side 2), make it into one big fraction and factor the top and bottom 3), find out the critical points (numerator = 0 and denominator = 0) draw them on a number line 4), you plug in any number that is between the critical points and check for the sign 5), the one you are looking for > or < will be the answer

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2I just saw your reply lol the answer will be 0<x<1984 because x > 0

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.2but it's ok, we did not waste any time at all. this is exactly how you can solve these inequalities.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hahahah u r using what anwar taught u xD

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and yes VERYYYY much im applying them to my problems like RITE now lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes! thank you very much for your help :)
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