Question

Solve for n: −np − 3 ≥ 7(c − 4)

Answer 1

The first thing you need to do is distribute the 7 into the set of parenthesis on the right.  That will give you $-np-3 \geq 7c-28$.  Then add 3 to both sides: $-np \geq 7c-25$.  Divide both sides by p to get $-n \geq \frac{7c-25}{p}$.  Now divide both sides by -1.  This is where the sign of inequality is going to change direction.  That's why I saved it til last so we could make a point  of making sure it gets done.  $n \leq -( \frac{7c-25}{p})$ and if you distribute the negative in your solution is $n \leq \frac{-7c+25}{p}$.  Or you could write the positive expression first, as many of us prefer: $n \leq \frac{25-7c}{p}$.  There you go!