To find the value of [tex]\( x \)[/tex] for the function [tex]\( f(x) = 5(4x - 9) \)[/tex] when [tex]\( f(x) = 75 \)[/tex], follow these steps:
1. Start with the given function and set it equal to 75:
[tex]\[
5(4x - 9) = 75
\][/tex]
2. Next, divide both sides of the equation by 5 to simplify:
[tex]\[
4x - 9 = \frac{75}{5}
\][/tex]
[tex]\[
4x - 9 = 15
\][/tex]
3. To isolate the term with [tex]\( x \)[/tex], add 9 to both sides of the equation:
[tex]\[
4x - 9 + 9 = 15 + 9
\][/tex]
[tex]\[
4x = 24
\][/tex]
4. Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 4:
[tex]\[
x = \frac{24}{4}
\][/tex]
[tex]\[
x = 6
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 6 \)[/tex].
Thus, the correct answer is [tex]\( \boxed{6} \)[/tex].
