How do you solve and graph the compound inequality #3x + 8 < 2# or #x + 12 > 2 - x#?

1 Answer
Jul 9, 2015

Answer:

#3x+8 < 2# or #x+12 > 2 -x#
for all possible Real values of #x#.

Draw a solid number line or shade the entire Cartesian plane for the solution set of #x#

Explanation:

Given
[1]#color(white)("XXXX")##3x+8 < 2#
or
[2]#color(white)("XXXX")##x+12 > 2 -x#

From [1]
#color(white)("XXXX")##3x < -6#
#color(white)("XXXX")##x < -2#

From [2]
#color(white)("XXXX")##2x > -10#
#color(white)("XXXX")##x > -5#

So the solution set for #x# all all values for which
#color(white)("XXXX")##color(red)(x < -2)# or #color(blue)(x > -5)#

Any value that is not #< -2#
will be #> -5#
(and visa versa).