Question

The equation 1/7n - 4n = 1/3n is true for all values of n where n ≠ 0. Is the equation an identity?

A) No; it is not true for all values of n.
B) No; the equation has no solution.
C) Yes; it is true for most values of n.
D) Yes; it is true for every possible value of n.

Answer 1

The equation 1/7n - 4n = 1/3n is not an identity because it is not true for all values of n.

Step-by-step explanation:

To determine whether the equation 1/7n - 4n = 1/3n is an identity, we need to check if it is true for all values of n where n ≠ 0. Let's simplify the equation:

1/7n - 4n = 1/3n

To simplify the left side, we need to find a common denominator for 1/7n. The common denominator is 7n, so the equation becomes:

(1/7n)(7n/7n) - 4n = 1/3n

Simplifying further:

1 - 4n(7n) = 1/3n

1 - 28n^2 = 1/3n

Now let's multiply both sides of the equation by 3n to eliminate the fraction:

3n - 84n^3 = 1

Now we can see that the equation is not true for all values of n because it involves a cubic term (n^3). Therefore, the answer is A) No; it is not true for all values of n.