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!