How do you solve #-5 > -5-3w#?

1 Answer
Sep 1, 2015

Answer:

#w>0#

Explanation:

Right from the start, you can say that you need #w# to be positive because any negative value of #w# would make the product #(-3 * w)# positive, which in turn will make the right-hand side of the inequality bigger than #(-5)#.

SInce you need the left-hand side of the inequality to be strictly greater than the right-hand side, you cannot have #w=0#, since that would imply that

#-5 > -5 - 3 * 0#

#-5color(red)(cancel(color(black)(>)))-5#

So, the solution set for this inequality is #w>0#.

#-5 > -5 - 3w#

#-color(red)(cancel(color(black)(5))) + color(red)(cancel(color(black)(5))) > -3w#

#0 > -3w implies w > 0#