Math / Algebra

QuestionGiven $f(x)=-4 x-2$ , solve for $x$ whén $f(x)=6$ .

Studdy Solution

STEP 1

What is this asking? We're given a simple equation and need to find the mystery $x$ that makes $f(x)$ equal to $6$ . Watch out! Don't mix up $f(x)$ and $x$ . $f(x)$ is the output when we plug $x$ into our little function machine.

STEP 2

1. Set up the equation
2. Isolate $x$
3. Find $x$

STEP 3

Alright, so we know that $f(x) = -4x - 2$ , and we're told that $f(x) = 6$ .
This is like having two puzzle pieces that fit together perfectly!

STEP 4

Let's snap those pieces together to get $-4x - 2 = 6$ .
Boom! Now we have an equation we can work with.

STEP 5

Our goal is to get $x$ all alone on one side of the equation.
First, let's kick that $-2$ to the other side.
We can do this by adding $2$ to both sides of the equation:
$-4x - 2 + 2 = 6 + 2$ $-4x = 8$

STEP 6

See how the $-2$ on the left side disappears by adding to zero?
Magic! Now, we just need to detach that $-4$ from the $x$ .

STEP 7

Since $-4$ is multiplied by $x$ , we can divide both sides by $-4$ to divide to one:
$\frac{-4x}{-4} = \frac{8}{-4}$ $x = -2$

STEP 8

And there you have it!
We've isolated $x$ , and it's equal to $-2$ .
That's our final answer!

STEP 9

$x = -2$

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QuestionGiven $f(x)=-4 x-2$ , solve for $x$ whén $f(x)=6$ .

Studdy Solution

STEP 1

What is this asking? We're given a simple equation and need to find the mystery $x$ that makes $f(x)$ equal to $6$ . Watch out! Don't mix up $f(x)$ and $x$ . $f(x)$ is the output when we plug $x$ into our little function machine.

STEP 2

1. Set up the equation
2. Isolate $x$
3. Find $x$

STEP 3

Alright, so we know that $f(x) = -4x - 2$ , and we're told that $f(x) = 6$ .
This is like having two puzzle pieces that fit together perfectly!

STEP 4

Let's snap those pieces together to get $-4x - 2 = 6$ .
Boom! Now we have an equation we can work with.

STEP 5

Our goal is to get $x$ all alone on one side of the equation.
First, let's kick that $-2$ to the other side.
We can do this by adding $2$ to both sides of the equation:
$-4x - 2 + 2 = 6 + 2$ $-4x = 8$

STEP 6

See how the $-2$ on the left side disappears by adding to zero?
Magic! Now, we just need to detach that $-4$ from the $x$ .

STEP 7

Since $-4$ is multiplied by $x$ , we can divide both sides by $-4$ to divide to one:
$\frac{-4x}{-4} = \frac{8}{-4}$ $x = -2$

STEP 8

And there you have it!
We've isolated $x$ , and it's equal to $-2$ .
That's our final answer!

STEP 9

$x = -2$

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QuestionGiven f(x)=−4x−2f(x)=-4 x-2f(x)=−4x−2, solve for xxx whén f(x)=6f(x)=6f(x)=6.

Studdy Solution

STEP 1

What is this asking? We're given a simple equation and need to find the mystery xxx that makes f(x)f(x)f(x) equal to 666. Watch out! Don't mix up f(x)f(x)f(x) and xxx. f(x)f(x)f(x) is the *output* when we plug xxx into our little function machine.

STEP 2

1. Set up the equation2. Isolate xxx3. Find xxx

STEP 3

Alright, so we know that f(x)=−4x−2f(x) = -4x - 2f(x)=−4x−2, and we're told that f(x)=6f(x) = 6f(x)=6.This is like having two puzzle pieces that fit together perfectly!

STEP 4

Let's **snap those pieces together** to get −4x−2=6-4x - 2 = 6−4x−2=6.Boom! Now we have an equation we can work with.

STEP 5

Our goal is to get xxx all alone on one side of the equation.First, let's **kick that −2-2−2** to the other side.We can do this by adding 222 to both sides of the equation:−4x−2+2=6+2-4x - 2 + 2 = 6 + 2−4x−2+2=6+2−4x=8-4x = 8−4x=8

STEP 6

See how the −2-2−2 on the left side disappears by adding to zero?Magic! Now, we just need to **detach that −4-4−4** from the xxx.

STEP 7

Since −4-4−4 is *multiplied* by xxx, we can divide both sides by −4-4−4 to divide to one:−4x−4=8−4\frac{-4x}{-4} = \frac{8}{-4}−4−4x​=−48​x=−2x = -2x=−2

STEP 8

And there you have it!We've **isolated** xxx, and it's equal to −2-2−2.That's our **final answer**!

STEP 9

x=−2x = -2x=−2

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Studdy solves anything!

Start learning now

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QuestionGiven $f(x)=-4 x-2$ , solve for $x$ whén $f(x)=6$ .

What is this asking? We're given a simple equation and need to find the mystery $x$ that makes $f(x)$ equal to $6$ . Watch out! Don't mix up $f(x)$ and $x$ . $f(x)$ is the output when we plug $x$ into our little function machine.

1. Set up the equation
2. Isolate $x$
3. Find $x$

Alright, so we know that $f(x) = -4x - 2$ , and we're told that $f(x) = 6$ .
This is like having two puzzle pieces that fit together perfectly!

Let's snap those pieces together to get $-4x - 2 = 6$ .
Boom! Now we have an equation we can work with.

Our goal is to get $x$ all alone on one side of the equation.
First, let's kick that $-2$ to the other side.
We can do this by adding $2$ to both sides of the equation:
$-4x - 2 + 2 = 6 + 2$ $-4x = 8$

See how the $-2$ on the left side disappears by adding to zero?
Magic! Now, we just need to detach that $-4$ from the $x$ .

Since $-4$ is multiplied by $x$ , we can divide both sides by $-4$ to divide to one:
$\frac{-4x}{-4} = \frac{8}{-4}$ $x = -2$

And there you have it!
We've isolated $x$ , and it's equal to $-2$ .
That's our final answer!

$x = -2$