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 June 27th, 2010, 12:46 PM #1 Newbie   Joined: Jun 2010 Posts: 22 Thanks: 0 inequality What the way I can use to solve this inequality ? $2\cdot \left|2x^2+7x+5\right|+\left|8x+39\right|= 25 \ \ \ \$
 June 27th, 2010, 01:25 PM #2 Newbie   Joined: Jun 2010 Posts: 9 Thanks: 0 Re: inequality A general way to solve problems involving absolute values is to find the ranges for which each portion within absolute bars is positive or negative. For example, 8x + 39 ? 0 when x ? -4.875 2x^2 + 7x + 5 ? 0 for x ? -2.5 or x ? -1 We need to consider the equality (note: since the question is = 25, it is an equality, not an inequality) from the views of the first and second requirement sets. Now we consider the following equations. [x < -4.875] $2*(2x^{2}+7x+5)-(8x+39)=25$ [-4.875 < x ? -2.5 OR x ? -1] $2*(2x^{2}+7x+5)+(8x+39)=25$ [-2.5 < x < -1] $-2*(2x^{2}+7x+5)+(8x+39)=25$ Now that we have reduce the problem to simpler equalities (i.e., does not include absolute values) we can solve the readily. After doing that, check if the solutions fit within the given range. If they do, then you have your solution Hope that helps!
 June 27th, 2010, 05:52 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,386 Thanks: 2012 As it stands, it's an equation, not an inequality. Was it intended to include an "=" symbol? One can initially consider 2(2x² + 7x + 5) + 8x + 39 = 25, i.e., 2(x + 4)(2x + 3) = 0.

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