How do you solve #-5p - 14\leq - 2p - p#?

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Answer 1 · 2017-04-13T22:54:05

See the entire solution process below:

First combine like terms on the right side of the inequality:

#-5p - 14 <= -2p - 1p#

#-5p - 14 <= (-2 - 1)p#

#-5p - 14 <= -3p#

Next, add #color(red)(5p)# onto each side of the inequality to isolate the #p# term while keeping the inequality balanced:

#color(red)(5p) - 5p - 14 <= color(red)(5p) - 3p#

#0 - 14 <= (color(red)(5) - 3)p#

#-14 <= 2p#

Now, divide each side of the inequality by #color(red)(2)# to solve for #p# while keeping the equation balanced:

#(-14)/color(red)(2) <= 2p/color(red)(2)#

#-7 <= color(red)(cancel(color(black)(2)))p/cancel(color(red)(2))#

#-7 <= p#

To state the solution in terms of #p# we can reverse or "flip" the inequality:

#p >= -7#