Let's solve the inequality $2x \geq -12$.

Step-by-Step Solution:

1. Divide both sides by 2: $\frac{2x}{2} \geq \frac{-12}{2}$ Simplifying this: $x \geq -6$

Solution:

The solution is $x \geq -6$.

Graph of the Solution:

• This represents all values of $x$ that are greater than or equal to $-6$.
• On a number line, we place a closed circle at $-6$ (since it's included) and shade the line to the right, indicating that all numbers greater than or equal to $-6$ are part of the solution.

Would you like help with the graph or any other details?

Here are some related questions you can explore:

1. How would the solution change if the inequality was $2x > -12$?
2. What happens if you multiply or divide both sides of an inequality by a negative number?
3. How do you represent strict inequalities (e.g., $x > -6$) on a number line?
4. What is the difference between solving equations and inequalities?
5. How can this inequality be solved using interval notation?

Tip: Always remember to reverse the inequality sign when multiplying or dividing by a negative number.