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The problem in the image asks: "Which inequality is the union of \( x - 2 \geq 2x + 10 \)?"

To solve this, let's start by solving the inequality:

1. Start with the given inequality:
   \[
   x - 2 \geq 2x + 10
   \]

2. Subtract \( 2x \) from both sides:
   \[
   x - 2x - 2 \geq 10
   \]
   \[
   -x - 2 \geq 10
   \]

3. Add 2 to both sides:
   \[
   -x \geq 12
   \]

4. Multiply both sides by -1 (which reverses the inequality sign):
   \[
   x \leq -12
   \]

The inequality \( x \leq -12 \) is the solution. 

For the union, typically, you combine solutions from multiple inequalities, but since only one inequality is provided, the union would just be this single inequality.

If you have more questions or need further details, feel free to ask!

### Related Questions:
1. What happens to the inequality sign when you multiply both sides by a negative number?
2. How do you solve a compound inequality involving "and" or "or"?
3. What does the union of two inequalities represent graphically?
4. How would the solution change if the inequality were strict (e.g., \( x - 2 > 2x + 10 \))?
5. How can you check if a particular value satisfies an inequality?

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

Which inequality is the union of x - 2 >= 2x + 10?

Explore how to solve the inequality x - 2 >= 2x + 10 and learn the step-by-step process. This problem highlights key concepts such as inequalities and solving linear equations. Suitable for students in Grades 7-9.

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