Solve the equation below. What is the value of [tex]\( f \)[/tex]?

[tex]\[
\frac{A(3f + 6)}{2} = -3f + 10
\][/tex]

1. Subtract 3 from both sides.
2. Divide each side by [tex]\( 3f \)[/tex].
3. Add 3 to each side.
4. Multiply each side by [tex]\( 3f \)[/tex].



Answer :

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]