Let's simplify the expression step by step:

Given:  
\[
5(2x + 1) + 3(2 + 6x)
\]

1. Distribute the \(5\) across the terms inside the first parentheses:
\[
5(2x) + 5(1) = 10x + 5
\]

2. Distribute the \(3\) across the terms inside the second parentheses:
\[
3(2) + 3(6x) = 6 + 18x
\]

3. Now combine all the terms:
\[
10x + 5 + 6 + 18x
\]

4. Combine like terms (\(10x\) and \(18x\); \(5\) and \(6\)):
\[
(10x + 18x) + (5 + 6) = 28x + 11
\]

So, the simplified expression is:
\[
28x + 11
\]

Would you like more details or have any questions?

Here are 5 related questions to expand this:

1. How do you solve an equation like \( 5(2x+1) + 3(2+6x) = 0 \)?
2. What is the process for factoring linear expressions like \( 28x + 11 \)?
3. How can you solve the equation \( 28x + 11 = 0 \)?
4. Can you explain the distributive property in algebra?
5. How do you combine like terms in more complex expressions?

**Tip:** Always perform distribution first before combining like terms when simplifying expressions.

Learn how to simplify the expression 5(2x + 1) + 3(2 + 6x) with a step-by-step solution. This algebraic problem demonstrates key concepts such as the distributive property and combining like terms. Suitable for students in Grades 6-8.

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