Let's simplify the given expression:

\[
4w + 1 + w + 3w - 7
\]

1. Combine like terms (terms with \(w\)):

\[
4w + w + 3w = 8w
\]

2. Combine constants:

\[
1 - 7 = -6
\]

So, the simplified expression is:

\[
8w - 6
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What if the expression was \(4w + 2 + w + 3w - 5\)?
2. How would you solve the equation if it was set equal to zero: \(4w + 1 + w + 3w - 7 = 0\)?
3. How do you combine terms if there's a negative coefficient involved, like \( -4w + w + 3w - 7\)?
4. What happens if the expression includes fractions, like \( \frac{1}{2}w + 3w - 4\)?
5. Can you simplify expressions with variables and multiple parentheses?

**Tip:** When simplifying algebraic expressions, always combine like terms step by step, starting with variables and then constants.

Simplify the algebraic expression 4w + 1 + w + 3w - 7 step by step. Learn how to combine like terms and constants to reduce the expression to 8w - 6. Ideal for students in Grades 6-8 who are learning algebra and simplifying expressions.

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