Question

For what value of n is 3 3/4 - n = 1/2 + n?

(A) 1/2
(B) 7/8
(C) 15/16
(D) 31/32

Answer 1

To find the value of n in the equation 3 3/4 - n = 1/2 + n, we can convert the mixed numbers to improper fractions, combine like terms, find a common denominator, and solve for n by cross-multiplying.

Step-by-step explanation:

To find the value of n that satisfies the equation 3 3/4 - n = 1/2 + n, we need to isolate n on one side of the equation. First, let's convert the mixed numbers to improper fractions: 15/4 - n = 1/2 + n. Next, let's combine like terms by adding n to both sides of the equation: 15/4 - n + n = 1/2 + n + n. This simplifies to: 15/4 = 1/2 + 2n.

To eliminate the fractions, we need to find a common denominator. The common denominator between 4 and 2 is 4. Multiplying the numerator and denominator of 1/2 by 2 gives us 2/4. The equation then becomes: 15/4 = 2/4 + 2n.

Now we can combine the fractions on the right-hand side of the equation: 15/4 = (2 + 2n)/4. To solve for n, we can cross-multiply: 15 * 4 = 2 + 2n. Simplifying the equation gives us: 60 = 2 + 2n. Subtracting 2 from both sides gives us: 58 = 2n. Finally, dividing both sides by 2 gives us: n = 58/2 = 29.