https://file.aiquickdraw.com/mathbot/file/17265500091725jjn7x6t.jpg

The inequality provided in the image is:

\[
\frac{1}{2}x + 3 \geq 5x + 2
\]

### Let's solve this step by step:

1. **Subtract \( \frac{1}{2}x \) from both sides** to eliminate \( x \) on the left-hand side:
   \[
   3 \geq 5x - \frac{1}{2}x + 2
   \]
   
   Simplify the right side:
   \[
   3 \geq \left(5 - \frac{1}{2}\right)x + 2
   \]
   
   This simplifies to:
   \[
   3 \geq \frac{9}{2}x + 2
   \]

2. **Subtract 2 from both sides** to isolate the \( x \)-term:
   \[
   3 - 2 \geq \frac{9}{2}x
   \]
   Simplifies to:
   \[
   1 \geq \frac{9}{2}x
   \]

3. **Multiply both sides by \( \frac{2}{9} \)** to solve for \( x \):
   \[
   x \leq \frac{2}{9}
   \]

### Final Answer:
\[
x \leq \frac{2}{9}
\]

This is the solution to the inequality.

Would you like further details or clarification on any of these steps?

Here are 5 related questions you can explore:
1. How do you graph the solution to this inequality on a number line?
2. What happens to the inequality if you multiply or divide by a negative number?
3. Can you solve similar inequalities involving fractions and variables?
4. How would you approach solving a quadratic inequality?
5. How can this inequality be represented as a system of linear inequalities?

**Tip:** Always reverse the inequality symbol when multiplying or dividing both sides by a negative number in an inequality.

Solve the inequality: 1/2x + 3 ≥ 5x + 2.

Learn how to solve the linear inequality 1/2x + 3 ≥ 5x + 2 with a step-by-step explanation. This problem covers essential algebraic techniques, such as isolating variables and applying properties of inequalities. Suitable for students in Grades 8-10.

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