solve for f.\n2 - \\frac{1}{4}f = f - \\frac{3}{4}f + 3\nf =

Explanation:

Step1: Simplify the right - hand side

Combine like terms on the right - hand side: (f-\frac{3}{4}f=\frac{4f - 3f}{4}=\frac{1}{4}f). The equation becomes (2-\frac{1}{4}f=\frac{1}{4}f + 3).

Step2: Move the terms with (f) to one side

Add (\frac{1}{4}f) to both sides: (2-\frac{1}{4}f+\frac{1}{4}f=\frac{1}{4}f+\frac{1}{4}f + 3). We get (2=\frac{1 + 1}{4}f+3), i.e., (2=\frac{2}{4}f+3). Simplify (\frac{2}{4}f) to (\frac{1}{2}f), so (2=\frac{1}{2}f+3).

Step3: Move the constant term

Subtract 3 from both sides: (2 - 3=\frac{1}{2}f+3 - 3). We have (-1=\frac{1}{2}f).

Step4: Solve for (f)

Multiply both sides by 2: (2\times(-1)=2\times\frac{1}{2}f).

Answer:

(f=-2)