 5, left parenthesis, minus, 9, q, plus, 7, right parenthesis, plus, 3, left parenthesis, 5, q, plus, 5, right parenthesis5(−9*q*+7)+3(5*q*+5)

Let's simplify the expression step-by-step:

Given expression:
\[
5(-9q + 7) + 3(5q + 5)
\]

### Step 1: Distribute the terms inside the parentheses

1. Distribute the \(5\) in the first term:
   \[
   5(-9q + 7) = 5 \times (-9q) + 5 \times 7 = -45q + 35
   \]

2. Distribute the \(3\) in the second term:
   \[
   3(5q + 5) = 3 \times 5q + 3 \times 5 = 15q + 15
   \]

### Step 2: Combine like terms

Now, add the terms together:

\[
-45q + 35 + 15q + 15
\]

Combine the \(q\) terms and the constant terms:

\[
(-45q + 15q) + (35 + 15) = -30q + 50
\]

### Final Simplified Expression:

\[
-30q + 50
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you factor a linear expression like \(-30q + 50\)?
2. What is the difference between distributing and factoring in algebra?
3. How do you solve a linear equation once it is simplified?
4. Can you explain how to simplify an expression with more than two terms?
5. What are like terms, and why is it important to combine them?

### Tip:
Always keep track of negative signs when distributing terms in an expression.

Learn how to simplify the algebraic expression 5(-9q + 7) + 3(5q + 5) with a step-by-step solution. This problem covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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