How do you solve and graph the compound inequality #–5 + 2n ≥–11# or #–6 – 10n > 44 # ?

1 Answer
May 9, 2015

(1) #-5 + 2x >= - 11 # -> #2x >+ -6 -> x >= -3#

(2) #-6 - 10x > 44# -># 10 x < -50 -> x < -5#

For graphing the system, use a double number line.

On the top number line, figure out the solution set #x >= -3#
On the bottom number line, figure out the solution set x < -5

------------------------------------|-3===========|0============

==============|-5-------------------------------|0----------------------

By superimposing the 2 number lines. we easily see the solution set of the system. That is the 2 intervals (-3, +infinity) and (-infinity, -5]. The end point -3 is included in the solution set.