To simplify the expression $-7(4x - 2) + 7x$, we can proceed with the following steps:

1. Distribute $-7$ across $(4x - 2)$: $-7 \cdot 4x + (-7) \cdot (-2) = -28x + 14$

2. Rewrite the expression with the distributed terms: $-28x + 14 + 7x$

3. Combine like terms $(-28x$ and $7x$): $-28x + 7x = -21x$

4. Write the simplified expression: $-21x + 14$

So, the simplified expression is: $-21x + 14$

Would you like further details or have any questions?

Here are five related questions that explore similar concepts:

1. How would you simplify $3(5x - 4) + 8x$?
2. What is the result of simplifying $-6(2x - 3) + 4x$?
3. Can you find the simplified form of $5(x + 7) - 3x$?
4. How would you simplify the expression $2(-3x + 5) + x$?
5. What steps are involved in simplifying $-4(3x - 6) + 5x$?

Tip: When simplifying expressions with distribution, always distribute each term carefully, then combine like terms at the end.