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

Jul 20, 2018

The zenith is ( 4/3 10/3 ),. and the region is $\downarrow$..

#### Explanation:

$y < - 2 x + 6 \Rightarrow 3 - \frac{y}{2} > x$,

$y < x + 2 \Rightarrow x > y - 2$. Combining,

$3 - \frac{y}{2} > x > y - 2 \Rightarrow 3 - \frac{y}{2} > y - 2 \Rightarrow y < \frac{10}{3}$.

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]}