# How do you solve the inequality -2x + 3y < -6?

Feb 29, 2016

Solution set: area below the line (-2x + 3y + 6 = 0).

#### Explanation:

Standard form: f(x) = -2x + 3y + 6 < 0 (1).
First, graph the Line -2x + 3y + 6 = 0 by its 2 intercepts
y-intercept --> x = 0, --> $y = - \frac{6}{3} = - 2$
x-intercept --> y = 0 --> $x = - \frac{6}{-} 2 = 3.$
Now, use origin as test point. Replace x = 0 and y = 0 into inequality (1). We get 6 < 0. Not true. Then the origin isn't on the solution set.
The solution set is the area below the Line.
graph{-2x + 3y + 6 = 0 [-10, 10, -5, 5]}