Question

How do you solve and graph the compound inequality `3v+1≤19` and `2v-3<-11` ?

Answer 1

(1) 3x + 1 <= 19 -> 3x = 18 --> x <= 6

(2) 2x - 3 < - 11 -> 2x < -8 -> x < -4

For graphing the system, use a double number line.
The top line figures out the solution set x <= 6
The bottom line figures out the solution set x < -4

============|=======|0===========|6----------------------

============| -4--------|0---------------------------------------------

By superimposing the 2 number lines, we easily see the common solution set of the system. It is the open interval (-infinity, -4).