N-10+9n-3 combining like terms
The Correct Answer and Explanation is :
To combine the expression ( N – 10 + 9N – 3 ), we first need to identify the like terms. Like terms are terms that have the same variable raised to the same power. In this expression, we can categorize the terms as follows:
- Terms with the variable ( N ):
- ( N )
- ( 9N )
- Constant terms:
- ( -10 )
- ( -3 )
Now, we can combine the like terms.
Step 1: Combine the ( N ) terms
Add the coefficients of the ( N ) terms together:
[
N + 9N = 1N + 9N = 10N
]
Step 2: Combine the constant terms
Add the constant terms together:
[
-10 – 3 = -13
]
Step 3: Write the final expression
Now that we have combined the like terms, we can write the expression as:
[
10N – 13
]
Explanation
Combining like terms is a fundamental skill in algebra that simplifies expressions and equations. The process helps to reduce complexity and makes it easier to work with mathematical statements. It involves identifying and grouping terms that share the same variable and exponent, as this allows us to consolidate the expression into a more manageable form.
For instance, in the expression ( N – 10 + 9N – 3 ), we began by categorizing ( N ) and ( 9N ) as like terms due to their shared variable ( N ). Their coefficients (1 and 9) were added together, resulting in ( 10N ). The constants ( -10 ) and ( -3 ) were also combined to yield ( -13 ).
The final result, ( 10N – 13 ), maintains the original mathematical relationships while presenting the expression in a clearer and more concise format. This simplification is not only important for solving equations but also for understanding relationships within algebraic expressions. Simplifying expressions enables easier manipulation for further operations, such as solving equations or graphing functions.