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 yehoram June 27th, 2010 12:46 PM

inequality

What the way I can use to solve this inequality ?

$2\cdot \left|2x^2+7x+5\right|+\left|8x+39\right|= 25 \ \ \ \$

 Kardestis June 27th, 2010 01:25 PM

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!

 skipjack June 27th, 2010 05:52 PM

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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