Final answer:
To simplify the linear expression 4x + 5(5x + 1), distribute and combine like terms to get 29x + 5. This involves multiplying 5 by each term inside the parenthesis and then adding the result to 4x.
Step-by-step explanation:
The student has asked to simplify the linear expression given by 4x + 5(5x + 1). To simplify, we perform the operation indicated inside the parentheses first before multiplying by the coefficient outside the parentheses, which is 5 in this case.
Initially, we have:
4x + 5(5x + 1) = 4x + (5 × 5x) + (5 × 1)
Simplify inside the parentheses:
4x + 25x + 5 = 29x + 5
So the expression 4x + 5(5x + 1) simplifies to 29x + 5. This is because you combine like terms, which in this case are the terms containing x.
Remember, the steps for simplifying expressions include: eliminate terms wherever possible to simplify the algebra, and then check the answer to see if it is reasonable.