# How do you solve and graph 3y+6<=2y?

Dec 16, 2017

See a solution process below:

#### Explanation:

Subtract $\textcolor{red}{6}$ and $\textcolor{b l u e}{2 y}$ from each side of the inequality to solve for $y$ while keeping the inequality balanced:

$3 y - \textcolor{b l u e}{2 y} + 6 - \textcolor{red}{6} \le 2 y - \textcolor{b l u e}{2 y} - \textcolor{red}{6}$

$\left(3 - \textcolor{b l u e}{2}\right) y + 0 \le 0 - 6$

$1 y \le - 6$

$y \le - 6$

To graph this we will draw a horizontal line at $- 6$ on the veritical axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade below the line because the inequality operator also contains a "less than" clause:

graph{y <= -6 [-30, 30, -15, 15]}