To find the value of [tex]\( x \)[/tex] for which [tex]\( (f - g)(x) = 0 \)[/tex], we first need to set up the expression for [tex]\( (f - g)(x) \)[/tex].
Given:
[tex]\[ f(x) = 16x - 30 \][/tex]
[tex]\[ g(x) = 14x - 6 \][/tex]
The function [tex]\( (f - g)(x) \)[/tex] is:
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]
Substitute the given functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into the above expression:
[tex]\[ (f - g)(x) = (16x - 30) - (14x - 6) \][/tex]
Now, simplify the equation by combining like terms:
[tex]\[ (f - g)(x) = 16x - 30 - 14x + 6 \][/tex]
[tex]\[ (f - g)(x) = (16x - 14x) + (-30 + 6) \][/tex]
[tex]\[ (f - g)(x) = 2x - 24 \][/tex]
We need to find the value of [tex]\( x \)[/tex] for which [tex]\( (f - g)(x) = 0 \)[/tex], so set [tex]\( 2x - 24 = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ 2x - 24 = 0 \][/tex]
[tex]\[ 2x = 24 \][/tex]
[tex]\[ x = \frac{24}{2} \][/tex]
[tex]\[ x = 12 \][/tex]
The value of [tex]\( x \)[/tex] that satisfies [tex]\( (f - g)(x) = 0 \)[/tex] is:
[tex]\[ \boxed{12} \][/tex]
