The expression is:

$3(w + 1) + 4(2w + 3)$

Let's expand and simplify it step by step.

Step 1: Expand both terms

$3(w + 1) = 3w + 3$ $4(2w + 3) = 8w + 12$

Step 2: Add the expanded terms together

$3w + 3 + 8w + 12$

Step 3: Combine like terms

$(3w + 8w) + (3 + 12) = 11w + 15$

Thus, the fully simplified expression is:

$11w + 15$

Do you want more details, or have any questions about the process?

Here are 5 related questions to expand your understanding:

1. What is the distributive property, and why is it used here?
2. How would the result change if the expression were $3(w - 1) + 4(2w + 3)$?
3. Can you factor the simplified expression $11w + 15$?
4. What happens if you set $w = 2$ in the original expression and the simplified result?
5. How does the process change if there were three terms instead of two?

Tip: Always distribute constants or coefficients before combining like terms for clarity.