Question

Solve the equation:

3/4 x + 3 - 2x = - 1/4 + 1/n x + 5

a. n = 5
b. n = 2
c. n = 3
d. n = 4

Answer 1

To solve the given equation 3/4 x + 3 - 2x = - 1/4 + 1/n x + 5, combine like terms on both sides, simplify the equation, equate the coefficients of x, and solve for n. The value of n that satisfies the equation is n = 4/5.

Step-by-step explanation:

To solve the given equation 3/4 x + 3 - 2x = - 1/4 + 1/n x + 5, we need to find the value of n that satisfies the equation. Let's solve it step by step:

1. Combine like terms on both sides of the equation. We get (3/4 - 2)x + 3 = -1/4 + 1/n x + 5.
2. Simplify the equation further. We get (3/4 - 2 - 1/n)x + 3 = -1/4 + 5.
3. Combine the constants on both sides. We get (3/4 - 2 - 1/n)x + 3 = 19/4.
4. Now, we can equate the coefficients of x on both sides of the equation. We get 3/4 - 2 - 1/n = 0.
5. Solve for n. We get 1/n = 2 - 3/4. Simplifying this, we get 1/n = 8/4 - 3/4 = 5/4. Taking the reciprocal, we get n = 4/5.

Therefore, the value of n that satisfies the equation is n = 4/5.