The expression in the image is:

$3(1 - 2(x)) + 5(3x - 2)$

Let's simplify this step by step using the distributive property:

Step 1: Apply the distributive property

Distribute the constants 3 and 5 across the terms inside the parentheses:

$3(1 - 2x) = 3 \cdot 1 - 3 \cdot 2x = 3 - 6x$ $5(3x - 2) = 5 \cdot 3x - 5 \cdot 2 = 15x - 10$

Step 2: Combine the simplified terms

Now combine the results from the first step:

$3 - 6x + 15x - 10$

Step 3: Combine like terms

Group the constants and the variable terms:

$(3 - 10) + (-6x + 15x) = -7 + 9x$

Thus, the simplified expression is:

$9x - 7$

Would you like more details on any step or have any questions?

Here are 5 related questions to expand on this:

1. How does the distributive property work for negative coefficients?
2. Can this expression be factored further?
3. What are like terms, and how do we combine them?
4. What is the significance of simplifying expressions in algebra?
5. How would this process change if we had exponents in the expression?

Tip: Always distribute carefully and check for sign errors, especially when dealing with negative coefficients.