Let's solve and simplify this expression step by step:

The given expression is:

$4x - 7(3x - 2)$

Step 1: Distribute $-7$ to the terms inside the parentheses

$-7(3x - 2) = -7 \cdot 3x + (-7 \cdot -2)$ $= -21x + 14$

Step 2: Substitute the distributed terms back into the expression

$4x - 21x + 14$

Step 3: Combine like terms

$(4x - 21x) + 14 = -17x + 14$

Final Simplified Expression:

$-17x + 14$

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Let me know if you want further clarification or additional details!

Follow-up Questions:

1. What does it mean to distribute in algebraic terms?
2. How do you combine like terms effectively?
3. Can this expression be graphed? If yes, how?
4. How would the process change if there were additional variables, e.g., $4x + y - 7(3x - 2)$?
5. How does this method apply to factoring instead of expanding?

Tip:

Always check your signs (positive and negative) carefully when distributing to avoid errors!