Answer
See below:
Work Step by Step
Step 1: Convert the inequality to an equation by replacing \[\ge \] by = sign.
\[2x+3y=12\]
Step 2: Graph the equation using intercept form or slope-intercept form.
Make \[x=0\] to find the y-intercept,
\[\begin{align}
& 2x+3y=12 \\
& 0+3y=12 \\
& y=4
\end{align}\]
Make \[y=0\] to find x-intercept,
\[\begin{align}
& 2x+3y=12 \\
& 2x+0=12 \\
& x=6
\end{align}\]
So, the line passes through \[\left( 6,0 \right)\]and \[\left( 0,4 \right)\]. The line is solid since the inequality contains the \[\ge \]symbol.
Step 3: Choose a test point. The origin \[\left( 0,0 \right)\]be the test point. Substituting in the inequality
\[\begin{align}
& 2x+3y\ge 12 \\
& 0\ge 12
\end{align}\]
The statement is false. The graph does not contain the test point.
