Math / Algebra

Question10.
If $f(x)=-6-12 x$ and $f(x)=18$ what is the value of $x$ ? A -222 B -2 C 2 D 222

Studdy Solution

STEP 1

What is this asking? We're given a simple equation, $f(x) = -6 - 12x$ , and told that the output of this equation, $f(x)$ , is equal to $18$ .
We need to find the input, $x$ , that makes this happen! Watch out! Be super careful with your signs when solving for $x$ .
One misplaced negative sign can lead you to the wrong answer!

STEP 2

1. Set up the equation
2. Isolate the term with $x$
3. Solve for $x$

STEP 3

We know that $f(x) = 18$ and $f(x) = -6 - 12x$ .
This means we can set them equal to each other!
So, we have $18 = -6 - 12x$ .
This is our starting point!

STEP 4

We want to get that $-12x$ term all by itself.
To do this, we need to add $6$ to both sides of the equation.
Remember, what we do to one side, we must do to the other!

STEP 5

So, $18 + 6 = -6 - 12x + 6$ .
This simplifies to $24 = -12x$ .
We're getting closer!

STEP 6

Now, we want to find the value of a single $x$ .
We currently have $-12$ times $x$ , so to get $x$ by itself, we need to divide both sides of the equation by $-12$ .

STEP 7

We have $\frac{24}{-12} = \frac{-12x}{-12}$ .
This simplifies to $-2 = x$ , or $x = -2$ .
We found it!

STEP 8

The value of $x$ that makes $f(x) = 18$ is $x = -2$ .
So the answer is B!

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Question10.
If $f(x)=-6-12 x$ and $f(x)=18$ what is the value of $x$ ? A -222 B -2 C 2 D 222

Studdy Solution

STEP 1

STEP 2

1. Set up the equation
2. Isolate the term with $x$
3. Solve for $x$

STEP 3

We know that $f(x) = 18$ and $f(x) = -6 - 12x$ .
This means we can set them equal to each other!
So, we have $18 = -6 - 12x$ .
This is our starting point!

STEP 4

We want to get that $-12x$ term all by itself.
To do this, we need to add $6$ to both sides of the equation.
Remember, what we do to one side, we must do to the other!

STEP 5

So, $18 + 6 = -6 - 12x + 6$ .
This simplifies to $24 = -12x$ .
We're getting closer!

STEP 6

Now, we want to find the value of a single $x$ .
We currently have $-12$ times $x$ , so to get $x$ by itself, we need to divide both sides of the equation by $-12$ .

STEP 7

We have $\frac{24}{-12} = \frac{-12x}{-12}$ .
This simplifies to $-2 = x$ , or $x = -2$ .
We found it!

STEP 8

The value of $x$ that makes $f(x) = 18$ is $x = -2$ .
So the answer is B!

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Question10.If f(x)=−6−12xf(x)=-6-12 xf(x)=−6−12x and f(x)=18f(x)=18f(x)=18 what is the value of xxx ? A -222 B -2 C 2 D 222

Studdy Solution

STEP 1

STEP 2

1. Set up the equation2. Isolate the term with xxx3. Solve for xxx

STEP 3

We know that f(x)=18f(x) = 18f(x)=18 and f(x)=−6−12xf(x) = -6 - 12xf(x)=−6−12x.This means we can set them equal to each other!So, we have 18=−6−12x18 = -6 - 12x18=−6−12x.This is our starting point!

STEP 4

We want to get that −12x-12x−12x term all by itself.To do this, we need to add 666 to both sides of the equation.Remember, what we do to one side, we *must* do to the other!

STEP 5

So, 18+6=−6−12x+618 + 6 = -6 - 12x + 618+6=−6−12x+6.This simplifies to 24=−12x24 = -12x24=−12x.We're getting closer!

STEP 6

Now, we want to find the value of a **single** xxx.We currently have −12-12−12 times xxx, so to get xxx by itself, we need to divide both sides of the equation by −12-12−12.

STEP 7

We have 24−12=−12x−12\frac{24}{-12} = \frac{-12x}{-12}−1224​=−12−12x​.This simplifies to −2=x-2 = x−2=x, or x=−2x = -2x=−2.We found it!

STEP 8

The value of xxx that makes f(x)=18f(x) = 18f(x)=18 is x=−2x = -2x=−2.So the answer is B!

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Studdy solves anything!

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Question10.
If $f(x)=-6-12 x$ and $f(x)=18$ what is the value of $x$ ? A -222 B -2 C 2 D 222

1. Set up the equation
2. Isolate the term with $x$
3. Solve for $x$

We know that $f(x) = 18$ and $f(x) = -6 - 12x$ .
This means we can set them equal to each other!
So, we have $18 = -6 - 12x$ .
This is our starting point!

We want to get that $-12x$ term all by itself.
To do this, we need to add $6$ to both sides of the equation.
Remember, what we do to one side, we must do to the other!

So, $18 + 6 = -6 - 12x + 6$ .
This simplifies to $24 = -12x$ .
We're getting closer!

Now, we want to find the value of a single $x$ .
We currently have $-12$ times $x$ , so to get $x$ by itself, we need to divide both sides of the equation by $-12$ .

We have $\frac{24}{-12} = \frac{-12x}{-12}$ .
This simplifies to $-2 = x$ , or $x = -2$ .
We found it!

The value of $x$ that makes $f(x) = 18$ is $x = -2$ .
So the answer is B!