How do you solve #5p - 3( p - 6) \leq 0#?

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Answer 1 · 2016-11-30T04:59:59

#p in (-oo, -9]#

#5p - 3(p-6) <= 0#

Apply the distributive property. #-3(p-6) = -3p+18#

#5p -3p + 18 <= 0#

Gather like terms. #5p-3p=2p#

#2p + 18 <= 0#

Isolate the term with #p# by subtracting #18# from both sides. Subtraction does not change the direction of the inequality.

#2p <= -18#

Isolate #p# by dividing both sides by #2#. As #2>0#, dividing by #2# does not change the direction of the inequality.

#p <= -9#

Thus, in set notation, or answer is

#p in (-oo, -9]#