Question

solve for f.
6 + 4f = 6(2f + 7) + 10f
f =

Explanation:

Step1: Expand the right side

First, we expand \(6(2f + 7)\) using the distributive property \(a(b + c)=ab+ac\). So, \(6(2f + 7)=6\times2f+6\times7 = 12f+42\). Then the equation becomes \(6 + 4f=12f + 42+10f\).

Step2: Combine like terms on the right

Combine \(12f\) and \(10f\) on the right side. \(12f+10f = 22f\), so the equation is now \(6 + 4f=22f + 42\).

Step3: Subtract \(4f\) from both sides

Subtract \(4f\) from each side to get \(6=22f - 4f+ 42\). Simplifying the right side, \(22f-4f = 18f\), so \(6 = 18f+42\).

Step4: Subtract 42 from both sides

Subtract 42 from each side: \(6 - 42=18f\). Calculating the left side, \(6 - 42=-36\), so \(-36 = 18f\).

Step5: Divide both sides by 18

Divide both sides by 18: \(\frac{-36}{18}=f\). Simplifying, \(f=- 2\).

Answer:

\(-2\)