The Correct Answer and Explanation is:
The correct simplified expression is c – 12.
To simplify the algebraic expression 5 + 3c – 2c – 17, you need to identify and combine the “like terms.” Like terms are the parts of the expression that have the same variable raised to the same power. In this problem, we have two types of terms: constant terms (the numbers) and terms with the variable ‘c’.
First, let’s identify and group the like terms together. It can be helpful to rearrange the expression to put similar terms next to each other.
Original expression: 5 + 3c – 2c – 17
Rearranged expression: (3c – 2c) + (5 – 17)
Now, we can simplify each group of like terms separately.
- Combine the ‘c’ terms:
We look at the part of the expression with the variable ‘c’, which is 3c – 2c. This means you have three ‘c’s and you subtract two ‘c’s. The calculation is (3 – 2)c, which equals 1c. In algebra, when the coefficient (the number in front of the variable) is 1, we usually do not write it. So, 1c is simply written as c. - Combine the constant terms:
Next, we look at the numbers without variables, which are 5 – 17. To solve this, you subtract 17 from 5. Since you are subtracting a larger number from a smaller one, the result will be negative. The difference between 17 and 5 is 12, so the result of this calculation is -12.
Finally, we put the simplified parts back together. From the ‘c’ terms, we got c. From the constant terms, we got -12. Combining these gives us the final simplified expression: c – 12.
This result matches the fourth option in the list.
