Solving the Equation: 3– 1/2 n = – 3/2 + 2– 1/4 n
In this article, we will solve the equation 3– 1/2 n = – 3/2 + 2– 1/4 n step by step.
Step 1: Simplify the Equation
First, we need to simplify the equation by combining like terms:
3 - 1/2 n = -3/2 + 2 - 1/4 n
Combine the constant terms:
3 - 3/2 + 2 = 7/2
So, the equation becomes:
-1/2 n - 1/4 n = 7/2
Step 2: Combine Like Terms
Next, we need to combine the like terms:
(-1/2 - 1/4) n = 7/2
To add these fractions, we need to find the least common multiple (LCM) of 2 and 4, which is 4. So, we can rewrite the fractions with a denominator of 4:
(-2/4 - 1/4) n = 7/2
Combine the fractions:
-3/4 n = 7/2
Step 3: Solve for n
Now, we need to solve for n:
-3/4 n = 7/2
Multiply both sides by -4/3 to get:
n = -7/3 × -4/3 n = 28/9
Therefore, the value of n is 28/9.
Conclusion
In this article, we have solved the equation 3– 1/2 n = – 3/2 + 2– 1/4 n step by step. The solution to the equation is n = 28/9.
