To determine the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\((f-g)(x) = 0\)[/tex], we need to follow these steps:
1. Start with the definitions of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
f(x) = 16x - 30
\][/tex]
[tex]\[
g(x) = 14x - 6
\][/tex]
2. Define the function [tex]\((f-g)(x)\)[/tex], which is the difference between [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
(f-g)(x) = f(x) - g(x)
\][/tex]
3. Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into this equation:
[tex]\[
(f-g)(x) = (16x - 30) - (14x - 6)
\][/tex]
4. Simplify the equation by distributing the subtraction:
[tex]\[
(f-g)(x) = 16x - 30 - 14x + 6
\][/tex]
5. Combine like terms:
[tex]\[
(f-g)(x) = (16x - 14x) + (-30 + 6)
\][/tex]
[tex]\[
(f-g)(x) = 2x - 24
\][/tex]
6. Set [tex]\((f-g)(x)\)[/tex] equal to 0 and solve for [tex]\( x \)[/tex]:
[tex]\[
2x - 24 = 0
\][/tex]
7. Add 24 to both sides of the equation:
[tex]\[
2x = 24
\][/tex]
8. Finally, divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 12
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\((f-g)(x) = 0\)[/tex] is [tex]\( 12 \)[/tex]. The correct option is:
[tex]\[
\boxed{12}
\][/tex]
