https://file.aiquickdraw.com/mathbot/file/17290119754465z0c4b8y.jpg

The inequality shown in the image is:

\[
\frac{x}{2} - \frac{y}{3} \geq -1
\]

Let's solve this step by step.

### Step 1: Eliminate the fractions.
Multiply every term in the inequality by the least common denominator (LCD) of 2 and 3, which is 6.

\[
6 \left(\frac{x}{2} - \frac{y}{3}\right) \geq 6 \cdot (-1)
\]

This gives:

\[
3x - 2y \geq -6
\]

### Step 2: Express the inequality.
The final inequality is:

\[
3x - 2y \geq -6
\]

This represents a linear inequality in two variables, describing a half-plane region in the coordinate plane.

Would you like to see the graph of this inequality or ask any further questions?

### Relative Questions:
1. How would you solve this inequality for a specific value of \( x \) or \( y \)?
2. Can you rewrite the inequality as an equation and graph the boundary line?
3. How do you test if a point lies within the solution set of this inequality?
4. What does the solution set look like in terms of the Cartesian plane?
5. How do the signs of the inequality affect the solution set (for instance, if it were \( < \) instead of \( \geq \))?

### Tip:
When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number.

Solve the inequality \( \frac{x}{2} - \frac{y}{3} \geq -1 \)

Learn how to solve the linear inequality \( \frac{x}{2} - \frac{y}{3} \geq -1 \) with step-by-step explanations. This solution involves eliminating fractions by multiplying through by the least common denominator and applying the rules of inequalities. Suitable for Grades 9-11 students.

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