https://file.aiquickdraw.com/mathbot/file/1728917195198ar7fl60l.jpg

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!

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Learn how to solve the linear inequality 5(x + 1) ≥ 4(x + 3) with a step-by-step solution. This problem covers algebraic concepts and the properties of inequalities. Suitable for Grades 7-9.

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