Let's simplify the expression step by step.

The expression is:

\[
-3(2x - y + 4z) + 5(x - 3y - (7x + z))
\]

### Step 1: Distribute the terms

Distribute \(-3\) across the first set of parentheses:

\[
-3(2x - y + 4z) = -6x + 3y - 12z
\]

Next, distribute \(5\) across the second set of parentheses. First, simplify the inside of the second parentheses:

\[
x - 3y - (7x + z) = x - 3y - 7x - z = -6x - 3y - z
\]

Now distribute \(5\) across:

\[
5(-6x - 3y - z) = -30x - 15y - 5z
\]

### Step 2: Combine all terms

Now add the two distributed expressions together:

\[
-6x + 3y - 12z + (-30x - 15y - 5z)
\]

Combine like terms:

\[
(-6x - 30x) + (3y - 15y) + (-12z - 5z)
\]

\[
-36x - 12y - 17z
\]

### Final simplified expression:

\[
-36x - 12y - 17z
\]

Would you like more details or have any questions?

Here are some related questions:
1. How do you apply the distributive property?
2. What are like terms in an algebraic expression?
3. How do you combine like terms in multi-variable expressions?
4. What is the importance of parentheses in algebraic expressions?
5. Can we simplify expressions with exponents similarly?

**Tip**: Always simplify the inner expressions inside parentheses first before distributing!

Simplify: -3(2x - y + 4z) + 5(x - 3y - (7x + z))

Simplify the algebraic expression -3(2x - y + 4z) + 5(x - 3y - (7x + z)) using the distributive property and combining like terms. This step-by-step guide walks through each part of the process and is ideal for students in Grades 8-10.

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