Question

solve for f.
$2 - \frac{1}{4}f = f - \frac{3}{4}f + 3$
$f = \square$

Explanation:

Step1: Eliminate denominators

Multiply all terms by 4:
$$4\times2 - 4\times\frac{1}{4}f = 4\times f - 4\times\frac{3}{4}f + 4\times3$$
$$8 - f = 4f - 3f + 12$$

Step2: Simplify like terms

Combine $f$ terms on the right:
$$8 - f = f + 12$$

Step3: Isolate $f$ terms

Add $f$ to both sides:
$$8 = 2f + 12$$

Step4: Isolate constant terms

Subtract 12 from both sides:
$$8 - 12 = 2f$$
$$-4 = 2f$$

Step5: Solve for $f$

Divide by 2:
$$f = \frac{-4}{2}$$

Answer:

$f = -2$