https://file.aiquickdraw.com/mathbot/file/1727640185638hjrhquqt.jpg

The problem presented in the image is:

\[
8x + 3 \geq -37
\]

Let's solve the inequality step-by-step.

### Step 1: Isolate the Variable
First, subtract 3 from both sides to isolate the term with \(x\):

\[
8x + 3 - 3 \geq -37 - 3
\]

\[
8x \geq -40
\]

### Step 2: Divide by 8
Now, divide both sides by 8 to solve for \(x\):

\[
x \geq \frac{-40}{8}
\]

\[
x \geq -5
\]

### Inequality Solution
The solution in inequality notation is:

\[
x \geq -5
\]

### Graphing on the Number Line
To graph this on a number line:

- Draw a number line that includes the point \(-5\).
- Use a solid circle at \(-5\) to indicate that \(-5\) is included in the solution (because it is "greater than or equal to").
- Shade the line to the right of \(-5\), indicating all numbers greater than or equal to \(-5\).

### Summary
- **Answer in Inequality Notation:** \( x \geq -5 \)

Would you like further clarification on the steps or help graphing it?

#### Related Questions:
1. How do you solve linear inequalities involving subtraction or addition?
2. How do you know when to use an open or closed circle on a number line?
3. How do you solve inequalities that involve multiplication by a negative number?
4. What are the differences between "greater than" and "greater than or equal to" in inequalities?
5. How can we verify if a specific value is a solution to an inequality?

**Tip:** Always remember that when multiplying or dividing both sides of an inequality by a negative number, you must flip the inequality sign.

Solve the inequality and graph the solution on the line provided: 8x + 3 ≥ -37.

Learn how to solve the linear inequality 8x + 3 ≥ -37 with a detailed step-by-step explanation and graph the solution on a number line. This problem covers basic algebraic concepts like inequality manipulation and graphical representation, suitable for students in Grades 7-9.

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