Question

How do you graph the inequality `y < -2x + 6` and `y< x + 2`?

Answer 1

See the triangular shaded region, for answer.
The zenith is ( 4/3 10/3 ),. and the region is `darr`..

Explanation:

`y < -2x + 6 rArr 3 - y / 2 > x`,

`y < x + 2 rArr x > y - 2`. Combining,

`3 - y/2 > x > y - 2 rArr 3 - y / 2 > y -2 rArr y < 10 / 3`.

The shaded triangular region below (4/3 10/3 ), sans the vertex, is

the answer. Note that the graph is the combined graph for

(y - x - 2)(y-6+2x)>0 that includes the graph for the the

reversed inequalities, as well.. The shaded triangular portion above

the vertex ( including the vertex ), has to be ignored..
graph{(y - x - 2)(y-6+2x)>0[-20/3 20/3 -10/3 10/3]}