https://file.aiquickdraw.com/mathbot/file/17261190061530kfad4ji.jpg

Let's carefully analyze the problem and identify the error.

The original inequality is:

\[
4 + 3(2x - 3) \geq 4x + 5
\]

### Step-by-step breakdown:

1. **Distribute the 3** in \( 3(2x - 3) \):
   \[
   4 + 6x - 9 \geq 4x + 5
   \]
2. **Combine like terms** on the left-hand side:
   \[
   6x - 5 \geq 4x + 5
   \]
3. **Move \( 4x \) to the left-hand side** by subtracting \( 4x \) from both sides:
   \[
   6x - 4x - 5 \geq 5
   \]
   Simplifying gives:
   \[
   2x - 5 \geq 5
   \]
4. **Add 5 to both sides**:
   \[
   2x \geq 10
   \]
5. **Divide both sides by 2**:
   \[
   x \geq 5
   \]

### Identifying the mistake:
The solution in the image shows:

\[
x \geq \frac{7}{3}
\]

which is incorrect. The correct inequality should be:

\[
x \geq 5
\]

### Answer:
The correct choice is:

- **The correct answer is \( x \geq 5 \); the person combined \( 4 + 6x \), which are not like terms.**

Do you want more details or have any other questions?

### Related questions:
1. Why is it important to combine like terms carefully in inequalities?
2. How do you reverse the inequality symbol when dividing by a negative number?
3. What are common mistakes to avoid when solving inequalities?
4. How can you check your solution to an inequality?
5. What happens to the inequality sign when multiplying or dividing by a negative number?

### Tip:
Always verify each step carefully in inequalities, especially when dealing with distributing, combining terms, and reversing inequality signs.

The problem below was solved incorrectly. Identify the error and the correct solution: 4 + 3(2x - 3) ≥ 4x + 5.

This page explains how to solve a linear inequality and correctly apply algebraic steps. It highlights a common mistake made in combining unlike terms and walks through the solution, showing how to handle inequalities properly. The problem is ideal for students in Grades 7-9.

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