I'm having a hard time solving this question:

(2t-10)/t > t + 5

I multiplied by the squared lowest common denominator value and tried to solve for x, except that I cannot find any real solutions. I'm not sure what else to do?

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- Nov 7th 2012, 12:46 PMmisiaizeskaSolving Rational Inequalities
I'm having a hard time solving this question:

(2t-10)/t > t + 5

I multiplied by the squared lowest common denominator value and tried to solve for x, except that I cannot find any real solutions. I'm not sure what else to do? - Nov 7th 2012, 01:01 PMMarkFLRe: Solving Rational Inequalities
$\displaystyle \frac{2t-10}{t}>t+5$

$\displaystyle 2-\frac{10}{t}>t+5$

$\displaystyle \frac{10}{t}+t+3<0$

$\displaystyle \frac{t^2+3t+10}{t}<0$

The numerator has no real roots (the discriminant is negative), so we only have the critical number $\displaystyle t=0$. So, test the expression on the two intervals:

$\displaystyle (-\infty,0)$ and $\displaystyle (0,\infty)$. If the expression is negative on either interval, then that interval is the solution.