Math / Algebra

QuestionSolve. $\sqrt[3]{6 x}=-2$
Select the correct choice below and, if necessary, fill in the answ A. The solution(s) is(are) $x=$ $\square$ (Type an integer or a simplified fraction. Use a comma to B. There is no solution.

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes the cube root of $6x$ equal to -2. Watch out! Remember that we can take the cube root of a negative number!

STEP 2

1. Isolate the Cube Root
2. Cube Both Sides
3. Solve for $x$

STEP 3

We already have the cube root isolated on one side of the equation: $\sqrt[3]{6x} = -2$ .
Great! Let's move on!

STEP 4

To get rid of the cube root, we're going to cube both sides of the equation.
This is like giving both sides of a seesaw a boost of the same strength!
Why? Because cubing a cube root "undoes" the cube root.
It's like multiplying by 3 and then dividing by 3.
We're left with what we started with!

STEP 5

$(\sqrt[3]{6x})^3 = (-2)^3$

STEP 6

On the left side, we have $(\sqrt[3]{6x})^3 = 6x$ .
On the right side, we have $(-2)^3 = -2 \cdot -2 \cdot -2 = -8$ .
So, our equation becomes: $6x = -8$

STEP 7

Now, we want to get $x$ all by itself.
It's currently being multiplied by 6.
To isolate $x$ , we need to divide both sides of the equation by 6.
Think of it like this: if 6 times $x$ is -8, then $x$ must be -8 divided by 6!

STEP 8

$\frac{6x}{6} = \frac{-8}{6}$

STEP 9

On the left side, the 6's divide to one, leaving just $x$ .
On the right side, we simplify the fraction $\frac{-8}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
So, $\frac{-8}{6}$ becomes $\frac{-4}{3}$ .

STEP 10

Therefore, our final result is: $x = -\frac{4}{3}$

STEP 11

The solution is $x = -\frac{4}{3}$ .
So, we choose A and fill in the box with $-\frac{4}{3}$ .

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QuestionSolve. $\sqrt[3]{6 x}=-2$
Select the correct choice below and, if necessary, fill in the answ A. The solution(s) is(are) $x=$ $\square$ (Type an integer or a simplified fraction. Use a comma to B. There is no solution.

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes the cube root of $6x$ equal to -2. Watch out! Remember that we can take the cube root of a negative number!

STEP 2

1. Isolate the Cube Root
2. Cube Both Sides
3. Solve for $x$

STEP 3

We already have the cube root isolated on one side of the equation: $\sqrt[3]{6x} = -2$ .
Great! Let's move on!

STEP 4

To get rid of the cube root, we're going to cube both sides of the equation.
This is like giving both sides of a seesaw a boost of the same strength!
Why? Because cubing a cube root "undoes" the cube root.
It's like multiplying by 3 and then dividing by 3.
We're left with what we started with!

STEP 5

$(\sqrt[3]{6x})^3 = (-2)^3$

STEP 6

On the left side, we have $(\sqrt[3]{6x})^3 = 6x$ .
On the right side, we have $(-2)^3 = -2 \cdot -2 \cdot -2 = -8$ .
So, our equation becomes: $6x = -8$

STEP 7

Now, we want to get $x$ all by itself.
It's currently being multiplied by 6.
To isolate $x$ , we need to divide both sides of the equation by 6.
Think of it like this: if 6 times $x$ is -8, then $x$ must be -8 divided by 6!

STEP 8

$\frac{6x}{6} = \frac{-8}{6}$

STEP 9

On the left side, the 6's divide to one, leaving just $x$ .
On the right side, we simplify the fraction $\frac{-8}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
So, $\frac{-8}{6}$ becomes $\frac{-4}{3}$ .

STEP 10

Therefore, our final result is: $x = -\frac{4}{3}$

STEP 11

The solution is $x = -\frac{4}{3}$ .
So, we choose A and fill in the box with $-\frac{4}{3}$ .

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QuestionSolve. 6x3=−2\sqrt[3]{6 x}=-236x​=−2Select the correct choice below and, if necessary, fill in the answ A. The solution(s) is(are) x=x=x= □\square□ (Type an integer or a simplified fraction. Use a comma to B. There is no solution.

Studdy Solution

STEP 1

What is this asking? We need to find the value of xxx that makes the cube root of 6x6x6x equal to -2. Watch out! Remember that we can take the cube root of a negative number!

STEP 2

1. Isolate the Cube Root2. Cube Both Sides3. Solve for xxx

STEP 3

We already have the cube root isolated on one side of the equation: 6x3=−2\sqrt[3]{6x} = -236x​=−2.Great! Let's move on!

STEP 4

To get rid of the cube root, we're going to **cube both sides** of the equation.This is like giving both sides of a seesaw a boost of the same strength!Why? Because cubing a cube root "undoes" the cube root.It's like multiplying by 3 and then dividing by 3.We're left with what we started with!

STEP 5

(6x3)3=(−2)3 (\sqrt[3]{6x})^3 = (-2)^3 (36x​)3=(−2)3

STEP 6

On the left side, we have (6x3)3=6x(\sqrt[3]{6x})^3 = 6x(36x​)3=6x.On the right side, we have (−2)3=−2⋅−2⋅−2=−8(-2)^3 = -2 \cdot -2 \cdot -2 = -8(−2)3=−2⋅−2⋅−2=−8.So, our equation becomes: 6x=−8 6x = -8 6x=−8

STEP 7

Now, we want to get xxx all by itself.It's currently being multiplied by **6**.To isolate xxx, we need to divide both sides of the equation by **6**.Think of it like this: if 6 times xxx is -8, then xxx must be -8 divided by 6!

STEP 8

6x6=−86 \frac{6x}{6} = \frac{-8}{6} 66x​=6−8​

STEP 9

On the left side, the 6's divide to one, leaving just xxx.On the right side, we simplify the fraction −86\frac{-8}{6}6−8​ by dividing both the numerator and the denominator by their **greatest common divisor**, which is **2**.So, −86\frac{-8}{6}6−8​ becomes −43\frac{-4}{3}3−4​.

STEP 10

Therefore, our **final result** is: x=−43 x = -\frac{4}{3} x=−34​

STEP 11

The solution is x=−43x = -\frac{4}{3}x=−34​.So, we choose A and fill in the box with −43-\frac{4}{3}−34​.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve. $\sqrt[3]{6 x}=-2$
Select the correct choice below and, if necessary, fill in the answ A. The solution(s) is(are) $x=$ $\square$ (Type an integer or a simplified fraction. Use a comma to B. There is no solution.

What is this asking? We need to find the value of $x$ that makes the cube root of $6x$ equal to -2. Watch out! Remember that we can take the cube root of a negative number!

1. Isolate the Cube Root
2. Cube Both Sides
3. Solve for $x$

We already have the cube root isolated on one side of the equation: $\sqrt[3]{6x} = -2$ .
Great! Let's move on!

To get rid of the cube root, we're going to cube both sides of the equation.
This is like giving both sides of a seesaw a boost of the same strength!
Why? Because cubing a cube root "undoes" the cube root.
It's like multiplying by 3 and then dividing by 3.
We're left with what we started with!

$(\sqrt[3]{6x})^3 = (-2)^3$

On the left side, we have $(\sqrt[3]{6x})^3 = 6x$ .
On the right side, we have $(-2)^3 = -2 \cdot -2 \cdot -2 = -8$ .
So, our equation becomes: $6x = -8$

Now, we want to get $x$ all by itself.
It's currently being multiplied by 6.
To isolate $x$ , we need to divide both sides of the equation by 6.
Think of it like this: if 6 times $x$ is -8, then $x$ must be -8 divided by 6!

$\frac{6x}{6} = \frac{-8}{6}$

On the left side, the 6's divide to one, leaving just $x$ .
On the right side, we simplify the fraction $\frac{-8}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
So, $\frac{-8}{6}$ becomes $\frac{-4}{3}$ .

Therefore, our final result is: $x = -\frac{4}{3}$

The solution is $x = -\frac{4}{3}$ .
So, we choose A and fill in the box with $-\frac{4}{3}$ .