Question 142663
All of these inequalities use the same principles as the arithmetic you already know with one additional thing to consider. That is, whenever you multiply or divide the equation by a negative number, the direction of the inequality changes.

So let's go step by step.
Given {{{-7x > 1/15}}}

First thing to do is to move the 7 from left side to right. To do that, divide both sides by 7

{{{(-7x)/7 > (1/15)/7}}}
{{{-x > 1/105}}}

Next, you need to get rid of the negative 1 (-1) on the left side. This time, multiply both sides by (-1)

{{{ (-1)(-x) < (-1)*(1/105)}}}  notice we changed the direction of the inequality

{{{x < -1/105}}}