Question

Graph the solution to the inequality 2x-3y<18

Answer 1

<, > - dotted line

≤, ≥ - solid line

`2x-3y<18\qquad\text{subtract 2x from both sides}\\\\-3y<-2x+18\qquad\text{change the signs}\\\\3y>2x-18\qquad\text{divide both sides by 3}\\\\y>(2)/(3)x-6\\\\y=(2)/(3)x-6-\text{It's a linear function}\\\\for\ x=0\to y=(2)/(3)(0)-6=0-6=-6\to(0;\ -6)\\\\for\ x=6\to y=(2)/(3)(6)-6=2(2)-6=4-6=-2\to(6;\ -2)`