To determine the value of [tex]\(x\)[/tex] for which [tex]\((f - g)(x) = 0\)[/tex], we first need to express [tex]\((f - g)(x)\)[/tex] in terms of [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
We are given the functions:
[tex]\[ f(x) = 16x - 30 \][/tex]
[tex]\[ g(x) = 14x - 6 \][/tex]
We need to find the value of [tex]\(x\)[/tex] for which:
[tex]\[ (f - g)(x) = 0 \][/tex]
First, let's evaluate [tex]\((f - g)(x)\)[/tex]:
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]
Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ (f - g)(x) = (16x - 30) - (14x - 6) \][/tex]
Next, simplify the expression inside the parentheses:
[tex]\[ (f - g)(x) = 16x - 30 - 14x + 6 \][/tex]
Combine like terms:
[tex]\[ (f - g)(x) = (16x - 14x) + (-30 + 6) \][/tex]
[tex]\[ (f - g)(x) = 2x - 24 \][/tex]
For [tex]\((f - g)(x) = 0\)[/tex], set the simplified expression equal to zero:
[tex]\[ 2x - 24 = 0 \][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[ 2x = 24 \][/tex]
[tex]\[ x = 12 \][/tex]
Therefore, the value of [tex]\(x\)[/tex] for which [tex]\((f - g)(x) = 0\)[/tex] is [tex]\( \boxed{12} \)[/tex].
