To simplify the expression \(5x + 2(1 + 4x)\), follow these steps:

1. **Distribute** the \(2\) across the terms inside the parentheses:
   \[
   5x + 2(1 + 4x) = 5x + 2 \cdot 1 + 2 \cdot 4x
   \]

2. **Multiply** the numbers:
   \[
   5x + 2 + 8x
   \]

3. **Combine like terms** (\(5x\) and \(8x\)):
   \[
   (5x + 8x) + 2 = 13x + 2
   \]

So, the simplified form of the expression is:

\[
\boxed{13x + 2}
\]

Would you like a detailed explanation, or do you have any questions?

Here are 5 related questions you might be interested in:
1. How do you simplify expressions with multiple parentheses?
2. What are like terms, and why do we combine them?
3. How do you distribute a negative number across a parentheses?
4. What are some common mistakes to avoid when simplifying expressions?
5. How can expressions with fractions be simplified?

**Tip:** When simplifying expressions, always follow the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to ensure accuracy.

Learn how to simplify the expression 5x + 2(1 + 4x) with a detailed step-by-step solution. 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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