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happyapple123
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x^2-4x<0 Inequalities 29 May 2020, 02:58
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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.

Can someone please assist? Thanks.

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Codebug4it
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x^2-4x<0 Inequalities 29 May 2020, 03:28
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happyapple123
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.

Can someone please assist? Thanks.
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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

\(0 < x < 4\)
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x^2-4x<0 Inequalities 29 May 2020, 04:44
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Thanks Codebug4it!
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x^2-4x<0 Inequalities 29 May 2020, 05:44
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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.

Can someone please assist? Thanks.
Show more

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.

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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!