The inequality you provided is:

$2x + 3y \geq 12$

This represents a linear inequality, and it can be interpreted as follows:

Steps to solve or interpret:

1. Graphing the inequality:

   • First, rewrite the inequality as an equation by replacing the inequality sign with an equal sign:

   $2x + 3y = 12$

   This is the equation of a straight line. To graph it, we can find two points by setting $x = 0$ and $y = 0$.

   • When $x = 0$:

   $3y = 12 \implies y = 4$

   This gives the point $(0, 4)$.

   • When $y = 0$:

   $2x = 12 \implies x = 6$

   This gives the point $(6, 0)$.

   Now, plot these two points and draw the line through them.

2. Inequality interpretation:

   • Since the inequality is $2x + 3y \geq 12$, the solution includes the line itself (because of the "equal to" part) and the region above the line (since we are considering greater than). To determine which side of the line satisfies the inequality, you can test a point not on the line, such as $(0, 0)$:

   $2(0) + 3(0) = 0 \geq 12$

   This is false, so the region that satisfies the inequality is on the opposite side of the origin.

Do you need more details or have any questions?

Here are five related questions you might find interesting:

1. How do you determine the slope of the line from the inequality $2x + 3y \geq 12$?
2. What happens when we change the inequality to $2x + 3y < 12$?
3. How would you solve a system of inequalities that includes $2x + 3y \geq 12$ and another inequality?
4. What are the possible values of $y$ if $x = 3$ in the inequality $2x + 3y \geq 12$?
5. How do you handle linear inequalities with fractions or decimals?

Tip:

When graphing inequalities, always check a point on either side of the boundary line to confirm which region satisfies the inequality.