Question

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

Answer 1

(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.