To solve the equation [tex]\(0.6f + 9g = 3g + f\)[/tex] for [tex]\(f\)[/tex] in terms of [tex]\(g\)[/tex], we will follow these steps:
1. Rewrite the equation:
[tex]\[
0.6f + 9g = 3g + f
\][/tex]
2. Move all terms involving [tex]\(f\)[/tex] to one side and all terms involving [tex]\(g\)[/tex] to the other side:
[tex]\[
0.6f + 9g - f = 3g
\][/tex]
[tex]\[
0.6f - f = 3g - 9g
\][/tex]
3. Combine like terms:
[tex]\[
-0.4f = -6g
\][/tex]
4. Solve for [tex]\(f\)[/tex]:
[tex]\[
f = \frac{-6g}{-0.4}
\][/tex]
5. Simplify the fraction:
[tex]\[
f = \frac{-6g}{-0.4} = \frac{6g}{0.4} = \frac{6g}{\frac{2}{5}} = 6g \cdot \frac{5}{2} = 15g
\][/tex]
Now we compare the calculated value of [tex]\(f\)[/tex] with the given choices:
1. [tex]\(f = \frac{-8g}{3}\)[/tex]
2. [tex]\(f = \frac{-6g}{5}\)[/tex]
3. [tex]\(f = \frac{-5g}{6}\)[/tex]
4. [tex]\(f = \frac{12g}{7}\)[/tex]
Notice that our calculated solution [tex]\(f = 15g\)[/tex] does not match any of the provided choices. Therefore, none of the given options is correct, based on our steps and calculation.
