https://file.aiquickdraw.com/mathbot/file/1730135803250b11ufhr1.jpg

To solve the inequality and identify the correct graph, let's analyze the inequality step-by-step:

### Given Inequality:
\[
-2x + 7 < 23
\]

### Step 1: Isolate \( x \)
1. **Subtract 7 from both sides:**
   \[
   -2x < 16
   \]
2. **Divide by -2** (and remember to reverse the inequality since we are dividing by a negative number):
   \[
   x > -8
   \]

### Solution Set
The solution to the inequality is:
\[
x > -8
\]

### Interpreting the Graph
- We are looking for a graph that represents \( x > -8 \), which should be an open circle at -8 (indicating that -8 is not included) and a line extending to the right (since \( x \) is greater than -8).
  
### Choosing the Correct Option
- **Option B** represents the correct solution. It shows an open circle at -8 and an arrow extending to the right.

### Answer:
The correct answer is **B**.

Would you like further details or have any questions?

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Here are five related questions to deepen understanding:
1. How do you handle inequalities when multiplying or dividing by a negative number?
2. What would the graph look like if the inequality was \( x \geq -8 \)?
3. How would the solution change if the inequality was \( -2x + 7 \leq 23 \)?
4. What if the inequality was \( 2x + 7 < 23 \) instead?
5. How can inequalities be represented on a number line when using intervals?

**Tip:** Remember, whenever dividing or multiplying by a negative in inequalities, flip the inequality sign!

Which graph represents the solution set of this inequality: -2x + 7 < 23?

Learn how to solve the inequality -2x + 7 < 23 and determine the correct graph for the solution. This problem involves solving inequalities and reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 7-9.

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