The image presents the following inequality:

$5(x + 1) \geq 4(x + 3)$

Let’s solve this step by step.

Step 1: Expand both sides

Expand the left-hand side and the right-hand side of the inequality:

$5(x + 1) = 5x + 5$ $4(x + 3) = 4x + 12$

Now the inequality becomes:

$5x + 5 \geq 4x + 12$

Step 2: Isolate the variable

Move all terms involving $x$ to one side and constants to the other:

$5x - 4x \geq 12 - 5$ $x \geq 7$

Step 3: Solution

The solution to the inequality is:

$x \geq 7$

Final Answer

The correct answer is $x \geq 7$.

Would you like more details or explanations on any step?

Here are 5 related questions for further practice:

1. How would you solve $3(x - 2) \leq 2(x + 4)$?
2. What is the solution to $6x - 9 \geq 3(x + 4)$?
3. Can you explain how inequalities change when both sides are divided by a negative number?
4. How would the solution change if the inequality was $5(x + 1) \leq 4(x + 3)$?
5. What is the meaning of strict inequalities like $x > 7$ compared to $x \geq 7$?

Tip: When solving inequalities, be careful when multiplying or dividing by negative numbers, as this reverses the inequality sign!