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# Inequality

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Manager
Joined: 03 Aug 2010
Posts: 105

Kudos [?]: 90 [0], given: 63

GMAT Date: 08-08-2011

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09 Oct 2010, 12:52
(10-w)(9-w)<9

Solve for w.

Simple arithmetic, but I am drawing a blank on solving for a variable in inequality.
Through trial and error, I figured out w, but can someone walk me through the system of solving for w.

Kudos [?]: 90 [0], given: 63

Retired Moderator
Joined: 02 Sep 2010
Posts: 794

Kudos [?]: 1155 [0], given: 25

Location: London

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09 Oct 2010, 17:03
Yalephd wrote:
(10-w)(9-w)<9

Solve for w.

Simple arithmetic, but I am drawing a blank on solving for a variable in inequality.
Through trial and error, I figured out w, but can someone walk me through the system of solving for w.

$$(10-w)(9-w) \lt 9$$
$$(w-9)(w-10) \lt 9$$
$$w^2-19w+90 \lt 9$$
$$w^2-19w+81 \lt 0$$
$$(w-P)(w-Q) \lt 0$$

P = (19+sqrt(37))/2
Q= (19-sqrt(37))/2

Solution is Q<w<P OR $$\frac{19-sqrt{37}}{2} < w < \frac{19+sqrt{37}}{2}$$
_________________

Kudos [?]: 1155 [0], given: 25

Re: Inequality   [#permalink] 09 Oct 2010, 17:03
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