https://file.aiquickdraw.com/mathbot/file/1726680457874qylyjivn.jpg

The problem in the image is an inequality:

\[
7x + 22 \geq 15
\]

To solve for \( x \), follow these steps:

1. **Subtract 22 from both sides:**

\[
7x + 22 - 22 \geq 15 - 22
\]
\[
7x \geq -7
\]

2. **Divide both sides by 7:**

\[
x \geq -1
\]

The solution is:

\[
x \geq -1
\]

### Graphing the solution:
The graph shows a number line, and since the inequality is \( x \geq -1 \), it will include:
- A **closed circle** at \( -1 \) (indicating that \( x = -1 \) is included).
- An arrow pointing to the right, representing all numbers greater than or equal to \( -1 \).

Do you want more details or have any questions?

Here are 5 related questions:
1. What happens if the inequality symbol were \( \leq \) instead of \( \geq \)?
2. How would the solution change if the equation were \( 7x + 22 > 15 \)?
3. How do we graph inequalities when dividing by a negative number?
4. Can you show how to check the solution to this inequality?
5. What is the general approach to solving linear inequalities?

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

7x + 22 ≥ 15. Solve the inequality and graph the solution.

Learn how to solve the linear inequality 7x + 22 ≥ 15 and graph the solution. Follow the step-by-step guide to understand the process of isolating x and representing the solution on a number line. Suitable for students in Grades 7-9.

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