10n = 40 ( solve for n )
The Correct Answer and Explanation is :
To solve the equation ( 10n = 40 ), we want to find the value of ( n ) that satisfies this equation.
Steps to solve:
- Understand the equation: The equation tells us that 10 times some number ( n ) equals 40. Our goal is to isolate ( n ), which means we want ( n ) on one side of the equation by itself.
- Isolate ( n ): To do that, we need to get rid of the 10 that’s being multiplied by ( n ). Since the operation is multiplication, we’ll do the opposite operation, which is division.
[
10n = 40
]
Divide both sides of the equation by 10:
[
\frac{10n}{10} = \frac{40}{10}
]
This simplifies to:
[
n = 4
]
So, the solution is ( n = 4 ).
Explanation:
In algebra, solving equations often involves isolating the variable (in this case, ( n )) on one side of the equation. Here, the variable ( n ) is being multiplied by 10, so we need to “undo” this operation to isolate ( n ). The opposite of multiplication is division, so dividing both sides of the equation by 10 gives us the value of ( n ).
Dividing is a valid step because whatever we do to one side of an equation, we must also do to the other side to keep the equation balanced. Think of an equation like a balance scale — whatever happens on one side must also happen on the other.
After dividing by 10, we see that ( n = 4 ). This means that if you multiply 4 by 10, the result will be 40, which satisfies the original equation.
This process of solving for a variable by performing opposite operations (multiplication/division, addition/subtraction) is fundamental in algebra and helps to find unknown values in equations.