https://file.aiquickdraw.com/mathbot/file/1726848543211w2os3i2u.jpg

The given inequality to solve is:

\[
2(x - 3) + 9 \geq x
\]

Let's solve this step-by-step:

1. **Expand the expression:**

   \[
   2x - 6 + 9 \geq x
   \]

2. **Simplify the constants:**

   \[
   2x + 3 \geq x
   \]

3. **Move \(x\) to one side:**

   Subtract \(x\) from both sides:

   \[
   2x - x + 3 \geq 0
   \]

   Simplify:

   \[
   x + 3 \geq 0
   \]

4. **Isolate \(x\):**

   Subtract 3 from both sides:

   \[
   x \geq -3
   \]

The correct answer is:

\[
\boxed{x \geq -3}
\]

Would you like a detailed explanation of each step? Here are some related questions you might find helpful:

1. How do you solve inequalities with variables on both sides?
2. What is the difference between solving equations and inequalities?
3. How does multiplying or dividing by negative numbers affect inequalities?
4. How can inequalities be represented on a number line?
5. What are common mistakes when solving inequalities?

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

Learn how to solve the inequality 2(x - 3) + 9 ≥ x with a step-by-step explanation. This problem covers algebraic concepts and inequalities. Suitable for students in Grades 8-10.

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