How do you solve #-24<= -6(-2p-8)#?

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Answer 1 · 2016-11-30T12:44:16

#p >= -6#

First, expand the term withing parenthesis. Remember a negative number times a negative number results in a positive number:

#-24 <= (-6*-2p) + (-6*-8)#

#-24 <= 12p + 48#

Now subtract 48 from each side of the inequality to isolate the #p# term and keep the inequality balanced:

#-24 - 48 <= 12p + 48 - 48#

#-72 <= 12p + 0#

#-72 <= 12p#

Now we need to divide each side of the equation by #12# to slve for #p# and keep the inequality balanced:

#(-72)/12 <= (12p)/12#

#-6 <= (cancel(12)p)/cancel(12)#

#-6 <= p#

Finally, to solve in terms of #p# we can reverse or flip the inequality:

#p >= -6#