Certainly! Let's solve the equation [tex]\( f = \frac{1}{9}(g + h - k) \)[/tex] step-by-step for [tex]\( g \)[/tex].
1. Start with the given equation:
[tex]\[
f = \frac{1}{9}(g + h - k)
\][/tex]
2. Eliminate the fraction by multiplying both sides by 9:
[tex]\[
9f = g + h - k
\][/tex]
3. Isolate [tex]\( g \)[/tex] by moving [tex]\( h \)[/tex] and [tex]\(-k \)[/tex] to the other side:
[tex]\[
g = 9f - h + k
\][/tex]
Now, let’s put in the given values [tex]\( f = 2 \)[/tex], [tex]\( h = 3 \)[/tex], and [tex]\( k = 5 \)[/tex] to find the value of [tex]\( g \)[/tex].
4. Substitute [tex]\( f = 2 \)[/tex], [tex]\( h = 3 \)[/tex], and [tex]\( k = 5 \)[/tex] into the solved equation [tex]\( g = 9f - h + k \)[/tex]:
[tex]\[
g = 9(2) - 3 + 5
\][/tex]
5. Perform the multiplication first:
[tex]\[
g = 18 - 3 + 5
\][/tex]
6. Carry out the addition and subtraction:
[tex]\[
g = 15 + 5
\][/tex]
[tex]\[
g = 20
\][/tex]
Therefore, the value of [tex]\( g \)[/tex] is [tex]\( 20 \)[/tex].
