To solve the inequality $-3 \geq \frac{x}{-2}$:

1. Start by isolating $x$ by eliminating the fraction. Multiply both sides by $-2$. Remember, when multiplying or dividing by a negative number in inequalities, the inequality sign flips.

   $-3 \times -2 \leq x$

2. Simplify:

   $6 \leq x$

3. This can be written as:

   $x \geq 6$

Answer in Inequality Notation:

The solution is: $x \geq 6$

Graphing the Solution on a Number Line:

To graph $x \geq 6$:

• Draw a number line.
• Place a closed dot at $6$ to indicate that $6$ is included in the solution.
• Shade the line to the right of $6$ to represent all values greater than or equal to $6$.

Would you like further details, or do you have any questions?

Here are some related questions:

1. What are the rules for flipping inequality signs in equations?
2. How do we interpret the inequality $x \geq 6$ in real-world contexts?
3. How do we graph inequalities on a number line effectively?
4. What are the common mistakes to avoid when solving inequalities?
5. How do you solve compound inequalities involving multiple steps?

Tip: When solving inequalities, always check if you need to flip the inequality sign, especially when multiplying or dividing by negative numbers.