Let's solve the given equation step-by-step to find the value of [tex]\( f \)[/tex]:
The given equation is:
[tex]\[
\frac{3(3f + 6)}{2} = -3f + 10
\][/tex]
First, let's clear the fraction by multiplying both sides of the equation by 2. This gives:
[tex]\[
3(3f + 6) = 2(-3f + 10)
\][/tex]
Next, distribute the terms inside the parentheses:
[tex]\[
9f + 18 = -6f + 20
\][/tex]
Now, we need to get all the [tex]\( f \)[/tex]-terms on one side and the constant terms on the other side. Let's first add [tex]\( 6f \)[/tex] to both sides:
[tex]\[
9f + 6f + 18 = 20
\][/tex]
Combine the [tex]\( f \)[/tex]-terms:
[tex]\[
15f + 18 = 20
\][/tex]
Next, subtract 18 from both sides to isolate the [tex]\( f \)[/tex]-term:
[tex]\[
15f = 2
\][/tex]
Now, divide both sides by 15:
[tex]\[
f = \frac{2}{15}
\][/tex]
So, the value of [tex]\( f \)[/tex] is:
[tex]\[
f = \frac{2}{15}
\][/tex]
