Question

How do you graph `a + b < 12` and `a - b >= 6`?

Answer 1

Solve the system of 2 variables
a + b < 12
`a - b >= 6`

Explanation:

Let call a = y and b = x to avoid confusion.
(1) y < - x + 12
(2)`y >= x + 6`

First, graph line y1 = - x + 12 by its 2 intercepts.
Make x = 0 -> y = 12. Make y = 0 -> x = 12.
The solution set of inequality (1) is the area below the line y1. Color or shade it.
Next graph line y2 = x + 6 by its 2 intercepts.
The solution set of (2) is the area above line y2. Color or shade it.
The compound solution set is the commonly shared area.
NOTE. The line y2 is included in the solution set
graph{-x + 12 [-10, 10, -5, 5]}
graph{x + 6 [-10, 10, -5, 5]}