How do you solve the inequality #2(w+4)>7(w-1)#?

1 Answer
Oct 3, 2016

Answer:

#w<3#

Explanation:

  1. Expand both sides:
    #2(w+4) = 2w+8#, and #7(w-1) = 7w-7#

  2. Bring all the variables on the left side, and all the constants on the right:
    #2w+8>7w-7 \implies 2w-7w> -7-8#

  3. Sum the terms:
    #-5w> -15#

  4. Divide both terms by #-5#. Note that when you deal with an inequality, if you multiply/divide both terms by a negative number you need to switch the inequality sign:
    #-5w> -15 \implies w< (-15)/(-5) =3#