How do you solve compound inequalities #p + 4 > 6# and #3p < -18#?

1 Answer
Alan P.
Jul 16, 2015

#p+4 > 6 and 3p < -18#
#color(white)("XXXX")##rArr 2 < p < -6# impossible
There are no values of #p# that satisfy this pair of compound inequalities

Explanation:

Evaluate the two inequalities separately

#p+4 > 6#
#color(white)("XXXX")##color(white)("XXXX")#Subtract 4 from each side
#color(white)("XXXX")##p > 2#
enter image source here

#3p < -6#
#color(white)("XXXX")##color(white)("XXXX")#Divide each side by 3
#color(white)("XXXX")##color(white)("XXXX")#(this is valid without modifying the orientation of the inequality, since 3 > 0)
#color(white)("XXXX")##p < -6#
enter image source here

#p+4 > 6# and #3p < -18#
are those values of #p# for which both conditions are true:
enter image source here

As we can see from the above number line,
there are no values for which both conditions are true.

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