To determine the value of [tex]\( x \)[/tex] for which [tex]\((f-g)(x) = 0\)[/tex], we start by defining [tex]\((f-g)(x)\)[/tex]:
[tex]\[
(f-g)(x) = f(x) - g(x)
\][/tex]
Given the functions [tex]\( f(x) = 16x - 30 \)[/tex] and [tex]\( g(x) = 14x - 6 \)[/tex], we can substitute these into the equation for [tex]\((f-g)(x)\)[/tex]:
[tex]\[
(f-g)(x) = (16x - 30) - (14x - 6)
\][/tex]
Now, let's simplify the expression:
[tex]\[
(f-g)(x) = 16x - 30 - 14x + 6
\][/tex]
Combine like terms:
[tex]\[
(f-g)(x) = (16x - 14x) + (-30 + 6)
\][/tex]
This simplifies to:
[tex]\[
(f-g)(x) = 2x - 24
\][/tex]
We want to find the value of [tex]\( x \)[/tex] for which [tex]\((f-g)(x) = 0\)[/tex]:
[tex]\[
2x - 24 = 0
\][/tex]
To solve for [tex]\( x \)[/tex], first add 24 to both sides of the equation:
[tex]\[
2x - 24 + 24 = 0 + 24
\][/tex]
This simplifies to:
[tex]\[
2x = 24
\][/tex]
Next, divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{24}{2}
\][/tex]
So, we have:
[tex]\[
x = 12
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies [tex]\((f-g)(x) = 0\)[/tex] is 12. Therefore, out of the given options, the correct answer is:
12
