When considering the equation (f – g)(x) = 0, we are essentially looking for the value of x that would make the difference between f(x) and g(x) equal to zero. To find this value, let’s start by understanding what f(x) and g(x) represent.

In this case, f(x) is defined as 16x – 30 and g(x) is defined as 14x – 6. To find the value of x where their difference equals zero, we need to subtract g(x) from f(x).

So, (f – g)(x) = (16x – 30) – (14x – 6).

By simplifying this expression further, we get:

(f – g)(x) = 16x – 30 – 14x + 6.

Combining like terms, we have:

(f – g)(x) = 2x -24.

Now that we have simplified our equation, let’s set it equal to zero:

2x -24 = 0.

To solve for x, we can add both sides by 24:

2x = 24.

Finally, dividing both sides by two gives us:

𝑥=12

Therefore, when (f-g)(𝑥)=0 in the given equation f(𝑥)=16𝑥−30 and g(𝑥)=14𝑥−6,the solution is 𝑥=12.

## if f(x) = 16x – 30 and g(x) = 14x – 6, for which value of x does (f – g)(x) = 0? –18 –12 12 18

### Finding the values of f(x) and g(x)

To understand the given functions, let’s first find the values of f(x) and g(x). The function f(x) is defined as 16x – 30, while g(x) is defined as 14x – 6.

Let’s substitute a value for x and calculate the respective values for both functions:

- For f(x), if we choose x = 1:
- f(1) = (16 * 1) – 30
- f(1) = 16 – 30
- f(1) = -14

- For g(x), if we choose x = 1:
- g(1) = (14 * 1) – 6
- g(1) = 14 – 6
- g(1) = 8

Therefore, when x is equal to one, f(x)= -14 and g(x)=8.

### Calculating (f – g)(x)

Now that we know the values of f(x) and g(x), let’s calculate (f-g)(x). To do this, we subtract the function g from the function f:

(f-g)(x)=f(x)-g(x)

Substituting in our previously calculated values: (f-g)(x)=(-14)-(8) (f-g)(x)=(-22)

So, (f-g)(x)= (-22).

### Solving for x when (f-g)(x)=0

Lastly, we need to determine at which value of x does (f-g)(x)=0. In other words, we are looking for the value of x where the difference between f and g equals zero.

Setting up an equation: (f-g)(x)=(16x-30)-(14x-6) 0=16x-30-14x+6 0=2x-24

Now, let’s solve for x:

2x-24=0 2x=24 x=12

Hence, the value of x when (f-g)(x)=0 is 12.

In conclusion, by understanding the given functions and performing calculations, we determined that for the expression (f-g)(x) to equal zero, the value of x must be 12.

## Evaluating the possible values of x

In order to find the value of x for which (f – g)(x) equals 0, we need to solve the equation (f – g)(x) = 0. Let’s break down this process step by step.

First, let’s substitute the given functions f(x) = 16x – 30 and g(x) = 14x – 6 into (f – g)(x):

(f – g)(x) = f(x) – g(x)

Replacing f(x) and g(x), we get:

(f – g)(x) = (16x – 30) – (14x – 6)

Now, let’s simplify the expression:

(f – g)(x) = 16x – 30 – 14x + 6

Combining like terms, we have:

(f – g)(x) = (16x – 14x ) + (-30 +6)

Simplifying further:

(f – g)(x) = 2x-24

Now that we have simplified our expression, we can set it equal to zero and solve for x:

2𝑥 −24=0

Adding 24 to both sides of the equation gives us:

2𝑥=24

Finally, dividing both sides by two yields:

𝑥=12

Therefore, the value of x for which (f – g)(𝑥)=0 is 𝑥=12.

To summarize:

- The given functions are f(𝑥)=16𝑥−30 and 𝑔(𝑥)=14𝑥−6.
- We substituted these functions into (f-g)(𝑥).
- After simplifying the expression, we obtained 𝑓(−g)=2𝑥−24.
- By setting 𝑓(−g) equal to zero and solving the resulting equation, we found that 𝑥=12 satisfies the condition (f-g)(𝑥)=0.

Please note that this explanation assumes a basic understanding of algebraic operations and equations.