Answer :
To determine the value of [tex]\( x \)[/tex] for which [tex]\((f - g)(x) = 0\)[/tex], we start by defining the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ f(x) = 16x - 30 \][/tex]
[tex]\[ g(x) = 14x - 6 \][/tex]
Next, we need to find [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]
Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ (f - g)(x) = (16x - 30) - (14x - 6) \][/tex]
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]
We are given that [tex]\((f - g)(x) = 0\)[/tex]. Therefore, we set the expression equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ 2x - 24 = 0 \][/tex]
Add 24 to both sides of the equation:
[tex]\[ 2x = 24 \][/tex]
Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{2} \][/tex]
[tex]\[ x = 12 \][/tex]
Thus, the value of [tex]\( x \)[/tex] for which [tex]\((f - g)(x) = 0\)[/tex] is [tex]\( \boxed{12} \)[/tex].
[tex]\[ f(x) = 16x - 30 \][/tex]
[tex]\[ g(x) = 14x - 6 \][/tex]
Next, we need to find [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]
Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ (f - g)(x) = (16x - 30) - (14x - 6) \][/tex]
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]
We are given that [tex]\((f - g)(x) = 0\)[/tex]. Therefore, we set the expression equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ 2x - 24 = 0 \][/tex]
Add 24 to both sides of the equation:
[tex]\[ 2x = 24 \][/tex]
Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{2} \][/tex]
[tex]\[ x = 12 \][/tex]
Thus, the value of [tex]\( x \)[/tex] for which [tex]\((f - g)(x) = 0\)[/tex] is [tex]\( \boxed{12} \)[/tex].
