https://file.aiquickdraw.com/mathbot/file/172646990910569fnzmnb.jpg

The expression in the image is:

\[
\frac{5(3x + 2)}{2}
\]

To simplify or expand this expression, follow these steps:

### Step 1: Distribute the 5 across the terms inside the parentheses.

\[
5(3x + 2) = 5 \cdot 3x + 5 \cdot 2 = 15x + 10
\]

### Step 2: Rewrite the expression with the distributed terms.

\[
\frac{15x + 10}{2}
\]

### Step 3: Simplify the fraction.

Each term in the numerator can be divided by 2:

\[
\frac{15x}{2} + \frac{10}{2} = \frac{15x}{2} + 5
\]

So the simplified expression is:

\[
\frac{15x}{2} + 5
\]

Would you like further explanation or have any specific questions about this?

Here are 5 related questions for further exploration:
1. How would you solve this expression if it were equal to zero?
2. How do you factor expressions like the one we started with?
3. How does distributing constants inside parentheses work with negative numbers?
4. What happens if the denominator was something other than 2?
5. How would you handle the same expression if there were an exponent?

**Tip**: When simplifying expressions, always look for common factors you can cancel to make the calculation easier.

Learn how to simplify the algebraic expression 5(3x + 2) divided by 2. This example demonstrates the distributive property and how to simplify fractions, suitable for students in Grades 7-9.

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