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

Question

1517 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-20T04:05:41

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

#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]}