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I keep trying to solve it but I seem to be making an error somewhere: $$4-\left|\frac{5y}{3}+4\right| > \frac25$$

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The big hint is that $|a|<b\Longleftrightarrow -b<a<b$. This is all that is needed here. – Andrés Caicedo Dec 22 '10 at 2:48
up vote 4 down vote accepted

$4-\left|\frac{5y}{3}+4\right| > \frac25$ can be rewritten as $-\left|\frac{5y}{3}+4\right| > \frac{-18}{5}$ or $\left|\frac{5y}{3}+4\right| < \frac{18}{5}$. From here, represent the expression as $\frac{-18}{5} < \frac{5y}{3}+4\ < \frac{18}{5}$ and proceed to solve it using arithmetic.

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you accidentally left the absolute value there in the last line – Zarrax Dec 22 '10 at 3:42
    
Thanks, I corrected it – InterestedGuest Dec 22 '10 at 3:54

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