Answer:
f = -2.
Explanation:
To solve for f in the equation 2 - 1/4f = f - 3/4f + 3, we can simplify and isolate the variable f.
Let's begin by simplifying the equation step by step:
2 - 1/4f = f - 3/4f + 3
We can start by simplifying the fractions:
2 - (1/4)f = (4/4)f - (3/4)f + 3
Next, let's combine like terms:
2 - (1/4)f = (1/4)f + 3
To eliminate the fractions, we can multiply both sides of the equation by the least common denominator (LCD), which is 4:
4(2 - (1/4)f) = 4((1/4)f + 3)
Simplifying further:
8 - f = f + 12
Now, we can isolate the variable f by moving all terms involving f to one side of the equation:
8 - f - f = 12
Combining like terms:
8 - 2f = 12
To solve for f, we can now isolate the variable:
-2f = 12 - 8
Simplifying:
-2f = 4
Finally, we can solve for f by dividing both sides of the equation by -2:
f = 4 / -2
Simplifying:
f = -2
Therefore, the solution to the equation is f = -2.