How do you solve and graph #-5<3p+7<=22#?

1 Answer
Alan P.
Jun 27, 2017

#color(red)(-4 < p <= 5)#
enter image source here

Explanation:

Remember that you can add or subtract any amount to all components of an inequality without changing the validity or orientation of the inequality.
Therefore
#color(white)("XXX")-5 < 3p+7 < 22#
after subtracting #7# from all components
#rarrcolor(white)("XX")-12 < 3p <= 15#

Also remember that you can multiply or divide all components of an inequality by any constant greater than zero without changing the validity or orientation of the inequality.
Therefore
#color(white)("XXX")-12 < 3p <= 15#
after dividing all components by #3#
#rarrcolor(white)("XX")-4 < p <= 5#

Note that in drawing the number line graph for this solution, an open circle is used at #(-4)# to indicate that this value is not included in the solution,
and a closed (or solid) circle is used at #(+5)# to indicate that this vale is included.

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