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If [tex]\( f(x) = 16x - 30 \)[/tex] and [tex]\( g(x) = 14x - 6 \)[/tex], for which value of [tex]\( x \)[/tex] does [tex]\( (f - g)(x) = 0 \)[/tex]?

A. [tex]\(-18\)[/tex]
B. [tex]\(-12\)[/tex]
C. 12
D. 18



Answer :

GinnyAnswer
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

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