Let's simplify the given expression:

\[
-(-9q + 30) + 6r - 2(-4r + 9q)
\]

### Step 1: Distribute the negative signs
Apply the negative signs and simplify:

\[
-(-9q + 30) = 9q - 30
\]
\[
-2(-4r + 9q) = 8r - 18q
\]

Now substitute back into the expression:

\[
9q - 30 + 6r + 8r - 18q
\]

### Step 2: Combine like terms
Group the terms involving \( q \) and \( r \):

\[
(9q - 18q) + (6r + 8r) - 30
\]

Simplify:

\[
-9q + 14r - 30
\]

### Final simplified expression:

\[
-9q + 14r - 30
\]

Would you like more details on any part of the process?

Here are some related questions you might find helpful:
1. How do you simplify expressions involving multiple variables?
2. What are the rules for distributing negative signs in algebra?
3. How do you group and combine like terms in an algebraic expression?
4. Can we solve this expression if we are given values for \( q \) and \( r \)?
5. How does the order of operations affect simplifying expressions?

**Tip:** Always distribute negative signs carefully to avoid mistakes in sign changes!

Learn how to simplify the algebraic expression -(-9q + 30) + 6r - 2(-4r + 9q) with a step-by-step explanation. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 7-9.

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