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# x^2-4x<0 Inequalities

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Intern
Joined: 10 Nov 2018
Posts: 9

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29 May 2020, 01:58
What is the range for the inequality x^2 - 4x <0?

The solution is 0<x<4.

But I think the solution should be x<0 x>4.

Manager
Joined: 01 Nov 2017
Posts: 106
Location: India
Schools: ISB '21
GMAT 1: 690 Q49 V36
GPA: 4
WE: Web Development (Consulting)

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29 May 2020, 02:28
happyapple123 wrote:
What is the range for the inequality x^2 - 4x <0?

The solution is 0<x<4.

But I think the solution should be x<0 x>4.

Hi happyapple123,

$$x^2 - 4x <0 => x (x - 4) < 0$$

This means either $$x < 0$$ or $$(x - 4) < 0$$ but not both, because if both are negative then multiplication of two negative numbers is positive so the equation will not be true.

Now, if
$$x < 0$$ then $$(x - 4)$$ is also less than 0, which makes both negative, so this cannot be true.

for example,

if $$x = -1$$, then $$(x - 4) => (-1 - 4) = -5 < 0$$
=> so, $$(-1) * (-5) = 5 > 0$$, so equation doesn't agree.

Hence, only $$(x - 4) < 0$$ but $$x > 0$$ which means

$$0 < x < 4$$
Intern
Joined: 10 Nov 2018
Posts: 9

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29 May 2020, 03:44
Thanks Codebug4it!
VP
Joined: 11 Feb 2015
Posts: 1177

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29 May 2020, 04:44
happyapple123 wrote:
What is the range for the inequality x^2 - 4x <0?

The solution is 0<x<4.

But I think the solution should be x<0 x>4.

If you think x<0 x>4. then the inequality must hold true for x= 1 and x = 5 and Not for x=2, right?

Plugin the value yourself, calculate and see for yourself what happens?

Whenever in doubt, you can test by plugging the values of x and consider various scenarios. You will get the answer yourself.
_________________
Manish
Re: x^2-4x<0 Inequalities   [#permalink] 29 May 2020, 04:44