Final answer:
The algebraic expression 5x + 7y + 4y + 16x is simplified by combining like terms, resulting in the simplified form 21x + 11y. We ensure the simplification is correct by comparing with the original, combining only like terms, checking arithmetic, and ensuring no further simplification is possible.
Step-by-step explanation:
The student is asking to simplify the algebraic expression 5x + 7y + 4y + 16x. To do this, we'll combine like terms. Like terms are terms that have the same variables raised to the same powers. Adding the coefficients of like terms, we get:
- Combine the x terms: 5x + 16x = 21x.
- Combine the y terms: 7y + 4y = 11y.
- Put them together to simplify the expression to: 21x + 11y.
By eliminating terms wherever possible and combining like terms, we have simplified the algebraic expression to 21x + 11y.
Steps for Checking if the Answer is Reasonable:
- Look at the original algebraic expression and the simplified version to ensure no terms have been missed.
- Make sure terms are legally combinable (only like terms can be combined).
- Check the arithmetic for any mistakes.
- Verify that the simplified expression is as reduced as possible.
After these steps, we can be confident that the answer provided, 21x + 11y, is reasonable and the algebra has been correctly simplified.