Let's simplify the given expression step by step:

The expression is:

$-6w - 4(5x - 3w) + 4x$

Step 1: Distribute the -4 to both terms inside the parentheses

$-4(5x - 3w) = -4 \cdot 5x + (-4) \cdot (-3w)$ $= -20x + 12w$

Now substitute this back into the expression:

$-6w - 20x + 12w + 4x$

Step 2: Combine like terms

• Combine the terms with $w$: $-6w + 12w = 6w$
• Combine the terms with $x$: $-20x + 4x = -16x$

Final result:

$6w - 16x$

Thus, the simplified expression is $6w - 16x$.

Would you like further clarification or details on any of the steps?

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Here are five related questions:

1. How do you simplify expressions with multiple variables?
2. What is the process of distributing a constant over parentheses?
3. How do you combine like terms when dealing with algebraic expressions?
4. What are some common mistakes when simplifying linear algebraic expressions?
5. How would you solve for one variable in an equation like this if given additional constraints?

Tip: When distributing a constant, always multiply it by every term inside the parentheses and keep the signs straight!