Let's simplify the given expression step by step:

Expression:

$-7(-3t + 5) + 4t$

Step 1: Distribute $-7$ across $(-3t + 5)$

$-7(-3t) + (-7)(5)$ Simplify each term: $21t - 35$

Step 2: Combine the distributed terms with $4t$

Now the expression becomes: $21t - 35 + 4t$

Combine like terms ($21t$ and $4t$): $(21 + 4)t - 35 = 25t - 35$

Final Answer:

$25t - 35$

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

Here are 5 related questions to explore further:

1. How would you simplify $-5(2t - 3) + 7t$?
2. What is the result of $3(4t + 2) - 6t$?
3. Can you simplify $-8(-t + 6) + 3t$?
4. How do you factorize $25t - 35$?
5. What is the value of $25t - 35$ when $t = 2$?

Tip: When simplifying expressions, always distribute negative signs carefully and combine like terms for accuracy.