# How do you solve the inequality -5/6d+8>13?

Jan 31, 2016

$d < - 6$
We start off with $\frac{- 5}{6} d + 8 > 13$.
My goal is to isolate $d$ on one side of the expression. My first step would be to subtract $8$ on both sides, making the expression now $\frac{- 5}{6} d > 5$.
Now, I want to get $d$ alone, so I would divide by $\frac{- 5}{6}$ on both sides, making the expression now show $d < \frac{5}{- \frac{5}{6}}$, which can be rewritten as $d < 5 \cdot \left(- \frac{6}{5}\right)$. The $- 5 \cdot \left(- \frac{6}{5}\right)$will divide out (like so:$\cancel{5} \cdot \left(- \frac{6}{\cancel{5}}\right)$), leaving $d < - 6$.
Please note that the sign changed when I divided $\frac{- 5}{6}$ on both sides. This is because when I multiply or divide by a negative number, the sign of the expression changes, from $<$ to $>$ or vice versa.