The image you provided shows the inequality $5(x+1) \geq 7x - 1$ and offers multiple-choice answers. Let's solve the inequality.

Step 1: Distribute the 5 on the left side.

$5(x + 1) = 5x + 5$ So the inequality becomes: $5x + 5 \geq 7x - 1$

Step 2: Move all terms involving $x$ to one side and constant terms to the other.

Subtract $5x$ from both sides: $5x + 5 - 5x \geq 7x - 1 - 5x$ This simplifies to: $5 \geq 2x - 1$

Step 3: Add 1 to both sides to isolate the term with $x$:

$5 + 1 \geq 2x$ $6 \geq 2x$

Step 4: Divide by 2 to solve for $x$:

$\frac{6}{2} \geq x$ $3 \geq x$

This can be rewritten as: $x \leq 3$

Conclusion:

The solution is $x \leq 3$. This corresponds to the answer option $\boxed{x \leq 3}$.

Would you like further details or have any questions about the solution?

Here are some related questions you might find useful:

1. How do you solve inequalities involving distribution?
2. What is the difference between solving equations and inequalities?
3. How do you graph the solution of $x \leq 3$ on a number line?
4. What happens if you multiply or divide by a negative number in an inequality?
5. How can you check if a solution to an inequality is correct?
6. How do you solve compound inequalities?
7. What are the rules for adding or subtracting terms in inequalities?
8. How can you solve inequalities that contain absolute values?

Tip: Always remember to reverse the inequality sign when multiplying or dividing by a negative number.