Let's begin by simplifying the expression from the image you provided:

$4(5x - 2) - 5(2x - 3)$

Step 1: Apply the distributive property

Distribute the constants $4$ and $-5$ to each term inside the parentheses:

$= 4 \times 5x - 4 \times 2 - 5 \times 2x + 5 \times 3$

This simplifies to:

$= 20x - 8 - 10x + 15$

Step 2: Combine like terms

Now, combine the terms involving $x$ and the constant terms:

$(20x - 10x) + (-8 + 15)$

$= 10x + 7$

Thus, the simplified expression is:

$10x + 7$

Would you like further clarification on any step or have any questions about this?

Here are some related questions:

1. How do you distribute a constant across terms inside parentheses?
2. What is the distributive property, and how is it applied in algebra?
3. How do you combine like terms in algebraic expressions?
4. What happens if you subtract terms like $10x - 20x$?
5. How do you handle equations that involve more than one variable?

Tip: Always double-check your distribution and combining of terms to avoid missing a sign change!