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

May 9, 2015

(1) $- 5 + 2 x \ge - 11$ -> $2 x > + - 6 \to x \ge - 3$

(2) $- 6 - 10 x > 44$ ->$10 x < - 50 \to x < - 5$

For graphing the system, use a double number line.

On the top number line, figure out the solution set $x \ge - 3$
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.