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To find the correct graph that represents the solutions to the inequality \(-5x + 8 \leq -7\), let's solve the inequality step-by-step:

### Step 1: Solve the Inequality
Start with the given inequality:
\[
-5x + 8 \leq -7
\]

Subtract 8 from both sides:
\[
-5x \leq -7 - 8
\]
\[
-5x \leq -15
\]

Now, divide both sides by \(-5\). Remember, when you divide by a negative number, you must flip the inequality sign:
\[
x \geq 3
\]

### Step 2: Interpret the Solution
The solution \( x \geq 3 \) means that the values of \( x \) are 3 and all numbers greater than 3.

### Step 3: Match with the Graph
We need to find a graph where the shading starts at 3 and extends to the right, including 3 as a solid dot (indicating it is included in the solution).

### Checking the Graphs:
1. **First Graph:** It represents \( x \leq 3 \). This does not match.
2. **Second Graph:** It shows \( x \geq 3 \), with a solid dot at 3 and shading to the right. This matches our solution.
3. **Third Graph:** It represents \( x < 3 \). This does not match.

### Conclusion:
The second graph correctly represents the inequality \( -5x + 8 \leq -7 \).

Would you like any further details, or do you have any questions?

### Related Questions:
1. How do you solve inequalities involving fractions?
2. What happens when you multiply or divide an inequality by a negative number?
3. How do you graph inequalities on a number line?
4. Can inequalities have multiple solutions, and how do you represent them?
5. How do you solve compound inequalities?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number!

Which graph represents the solutions to the inequality -5x + 8 ≤ -7?

Learn how to solve the inequality -5x + 8 ≤ -7 and find the correct graph representation. This example explains solving linear inequalities, including rules for dividing by negative numbers, and how to graph solutions on a number line. Suitable for students in Grades 7-10.

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