Question

104.c
solve each equation.
\left(\frac{1}{2}f - \frac{1}{3}\
ight) \cdot \frac{1}{4} = 2f + 1
answer
example: x=3; x=5
grade answer

Explanation:

Step1: Distribute the multiplication

Multiply \(\frac{1}{4}\) into the parentheses: \(\frac{1}{2}f \cdot \frac{1}{4}-\frac{1}{3} \cdot \frac{1}{4}=2f + 1\)
Simplify each term: \(\frac{1}{8}f-\frac{1}{12}=2f + 1\)

Step2: Eliminate fractions (optional, but easier)

Multiply every term by the least common multiple of 8 and 12, which is 24:
\(24 \cdot \frac{1}{8}f-24 \cdot \frac{1}{12}=24 \cdot 2f+24 \cdot 1\)
Simplify each term: \(3f - 2 = 48f+24\)

Step3: Move all f terms to one side

Subtract \(3f\) from both sides: \(3f - 3f-2 = 48f - 3f+24\)
Simplify: \(-2 = 45f+24\)

Step4: Move constant terms to the other side

Subtract 24 from both sides: \(-2 - 24 = 45f+24 - 24\)
Simplify: \(-26 = 45f\)

Step5: Solve for f

Divide both sides by 45: \(f=\frac{-26}{45}\)

Answer:

\(f = -\frac{26}{45}\)