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

1 Answer
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.