To find the value of [tex]\( x \)[/tex] when [tex]\( f(x) = 6 \)[/tex] for the given function [tex]\( f(x) = \frac{1}{2} x + 3 \)[/tex], follow these steps:
1. Set the function equal to 6:
[tex]\[
\frac{1}{2} x + 3 = 6
\][/tex]
2. Isolate the term with [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2} x + 3 = 6
\][/tex]
Subtract 3 from both sides of the equation:
[tex]\[
\frac{1}{2} x = 6 - 3
\][/tex]
[tex]\[
\frac{1}{2} x = 3
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], multiply both sides of the equation by 2:
[tex]\[
x = 3 \times 2
\][/tex]
[tex]\[
x = 6
\][/tex]
Thus, the value of [tex]\( x \)[/tex] when [tex]\( f(x) = 6 \)[/tex] is [tex]\( \boxed{6} \)[/tex].
