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In this image, you are asked to solve the inequality \( \frac{7}{8}x + 1 \geq -3 \) and graph the solution on a number line.

### Step-by-step solution:

1. **Start with the inequality**:
   \[
   \frac{7}{8}x + 1 \geq -3
   \]

2. **Isolate the term with \( x \)**:
   Subtract 1 from both sides to get rid of the constant on the left-hand side:
   \[
   \frac{7}{8}x \geq -3 - 1
   \]
   \[
   \frac{7}{8}x \geq -4
   \]

3. **Solve for \( x \)**:
   To eliminate the fraction, multiply both sides of the inequality by the reciprocal of \( \frac{7}{8} \), which is \( \frac{8}{7} \):
   \[
   x \geq -4 \times \frac{8}{7}
   \]
   \[
   x \geq \frac{-32}{7}
   \]

   So the solution is:
   \[
   x \geq \frac{-32}{7}
   \]
   \[
   x \geq -4.57 \, (\text{approx})
   \]

### Graphing the solution:
- On a number line, draw an open or closed circle at \( x = \frac{-32}{7} \) (or approximately \( -4.57 \)).
- Since the inequality is \( x \geq -4.57 \), shade the region to the right of \( x = -4.57 \), indicating all numbers greater than or equal to this value.

Would you like further clarification or any additional assistance?

Here are some related questions to consider:

1. How would the solution change if the inequality sign were \( > \) instead of \( \geq \)?
2. What are the steps to graphing a strict inequality \( x < a \) or \( x > a \) on a number line?
3. How do you handle inequalities that involve absolute values?
4. Can you provide an example where multiplying or dividing an inequality by a negative number affects the inequality?
5. What are some real-life situations where inequalities are used?

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

Solve the inequality \( \frac{7}{8}x + 1 \geq -3 \) and graph the solution on a number line.

Learn how to solve the linear inequality \( \frac{7}{8}x + 1 \geq -3 \) with a detailed step-by-step explanation. This problem involves key algebraic concepts and the properties of inequalities. Suitable for students in Grades 7-9.

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