Solve for value of n?
(2n)
(3n-5)
The Correct Answer and explanation is :
To solve for the value of ( n ) in the expression ( (2n)(3n – 5) ), we need to clarify the context of the problem. If we want to find ( n ) when the product equals zero, we set the equation as follows:
[
(2n)(3n – 5) = 0
]
According to the zero product property, if the product of two factors is zero, at least one of the factors must be zero. Thus, we can set each factor to zero and solve for ( n ):
- Setting the first factor to zero:
[
2n = 0
]
Dividing both sides by 2 gives:
[
n = 0
] - Setting the second factor to zero:
[
3n – 5 = 0
]
Adding 5 to both sides results in:
[
3n = 5
]
Dividing both sides by 3 gives:
[
n = \frac{5}{3}
]
Now, we have two potential solutions for ( n ):
[
n = 0 \quad \text{or} \quad n = \frac{5}{3}
]
Explanation
The expression ( (2n)(3n – 5) ) involves two factors: ( 2n ) and ( 3n – 5 ). To find values of ( n ) that make this expression equal to zero, we apply the zero product property, which states that if the product of two numbers equals zero, then at least one of the numbers must be zero.
In our case, we examine both factors individually. The first factor, ( 2n ), is zero when ( n ) itself is zero, indicating that there are no units in the context defined by ( n ). The second factor, ( 3n – 5 ), is linear, and solving for ( n ) shows that when ( n ) equals ( \frac{5}{3} ) (approximately 1.67), the second factor becomes zero, thus nullifying the product as well.
Both solutions provide valid instances where the original expression ( (2n)(3n – 5) ) evaluates to zero. In applications such as physics or economics, these values can represent specific critical points, such as equilibrium states or thresholds, which merit further investigation based on the broader context of the problem.