Final answer:
The expression 8.4k + 7.3 + 2.2 - 3.6k is simplified by combining like terms, resulting in 4.8k + 9.5. Each step involves adding coefficients and constant terms separately, ensuring the result is expressed to the proper number of significant figures.
Step-by-step explanation:
To simplify the expression 8.4k + 7.3 + 2.2 - 3.6k, we need to combine like terms. The like terms here are 8.4k and -3.6k, which are both coefficients of k. Adding 7.3 and 2.2 gives us another constant term to simplify. So the steps are:
- Combine the coefficients of k: 8.4k - 3.6k = 4.8k.
- Add the constant terms: 7.3 + 2.2 = 9.5.
- Combine the simplified terms: 4.8k + 9.5.
After simplifying the expression, we do not need to perform any more operations as there are no like terms to combine further. To check if the answer is reasonable, we can assess if the operations of addition and subtraction were performed correctly on the coefficients and constants, which in this case they were.
To express answers with the correct number of significant figures and proper units, we have to ensure that the terms in the original expression were given with appropriate precision. Here, each term had at least two digits after the decimal, so our simplified expression, which also has two decimal places, seems appropriate.