3n – (2+n) what value of n makes this expression equal to 6
The Correct Answer and Explanation is:
To solve the equation (3n – (2 + n) = 6), we need to simplify the expression on the left side and then isolate (n).
Step 1: Distribute and Combine Like Terms
First, distribute the negative sign through the parentheses:
[
3n – 2 – n = 6
]
Next, combine the like terms (3n) and (-n):
[
(3n – n) – 2 = 6
]
This simplifies to:
[
2n – 2 = 6
]
Step 2: Isolate (2n)
Now, we want to isolate (2n) by eliminating the constant on the left side. We can do this by adding 2 to both sides of the equation:
[
2n – 2 + 2 = 6 + 2
]
This simplifies to:
[
2n = 8
]
Step 3: Solve for (n)
To find (n), divide both sides by 2:
[
n = \frac{8}{2}
]
This gives us:
[
n = 4
]
Conclusion
Thus, the value of (n) that makes the expression (3n – (2 + n)) equal to 6 is (n = 4).
Explanation
In algebra, expressions can often be manipulated to isolate variables and solve equations. The initial step is to clear any parentheses by distributing or combining like terms, which makes the equation simpler. In this case, the left side was simplified from (3n – (2 + n)) to (2n – 2).
Next, isolating the variable involves rearranging the equation to get (n) by itself on one side. This often includes adding or subtracting constants from both sides, maintaining the balance of the equation. After isolating the term with (n), we divided to find the value.
This methodical approach to solving for (n) not only leads to the correct answer but also reinforces foundational algebra skills that are applicable to more complex equations. Thus, solving (3n – (2 + n) = 6) revealed that (n = 4) is the required solution.