QuestionSolve: $\sqrt[4]{\frac{1}{3} x - 8} = 2$ . Choose one: a. $x=72$ , b. $x=8$ , c. $x=\frac{10}{3}$ , d. $x=-2$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $\sqrt[4]{\frac{1}{3} x-8}=$ . We need to solve for $x$

STEP 2

First, we need to remove the fourth root from the equation. We can do this by raising both sides of the equation to the power of4.
$(\sqrt[4]{\frac{1}{} x-8})^4 =2^4$

STEP 3

implify both sides of the equation.
\frac{1}{3} x-8 =2^

STEP 4

Calculate the value of $2^4$ .
$\frac{1}{3} x-8 =16$

STEP 5

Next, we need to isolate the term with $x$ on one side of the equation. We can do this by adding8 to both sides of the equation.
$\frac{1}{3} x =16 +8$

STEP 6

Calculate the value of $16 +8$ .
$\frac{1}{3} x =24$

STEP 7

Finally, to solve for $x$ , we multiply both sides of the equation by3.
$x =24 \times3$

STEP 8

Calculate the value of $24 \times3$ .
$x =72$ So, the solution to the equation $\sqrt[4]{\frac{1}{3} x-8}=2$ is $x=72$ .

Was this helpful?

QuestionSolve: $\sqrt[4]{\frac{1}{3} x - 8} = 2$ . Choose one: a. $x=72$ , b. $x=8$ , c. $x=\frac{10}{3}$ , d. $x=-2$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $\sqrt[4]{\frac{1}{3} x-8}=$ . We need to solve for $x$

STEP 2

First, we need to remove the fourth root from the equation. We can do this by raising both sides of the equation to the power of4.
$(\sqrt[4]{\frac{1}{} x-8})^4 =2^4$

STEP 3

implify both sides of the equation.
\frac{1}{3} x-8 =2^

STEP 4

Calculate the value of $2^4$ .
$\frac{1}{3} x-8 =16$

STEP 5

Next, we need to isolate the term with $x$ on one side of the equation. We can do this by adding8 to both sides of the equation.
$\frac{1}{3} x =16 +8$

STEP 6

Calculate the value of $16 +8$ .
$\frac{1}{3} x =24$

STEP 7

Finally, to solve for $x$ , we multiply both sides of the equation by3.
$x =24 \times3$

STEP 8

Calculate the value of $24 \times3$ .
$x =72$ So, the solution to the equation $\sqrt[4]{\frac{1}{3} x-8}=2$ is $x=72$ .

Get Studdy

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: 13x−84=2\sqrt[4]{\frac{1}{3} x - 8} = 2431​x−8​=2. Choose one: a. x=72x=72x=72, b. x=8x=8x=8, c. x=103x=\frac{10}{3}x=310​, d. x=−2x=-2x=−2.

Studdy Solution

STEP 1

Assumptions1. The equation is 13x−84=\sqrt[4]{\frac{1}{3} x-8}=431​x−8​= . We need to solve for xxx

STEP 2

First, we need to remove the fourth root from the equation. We can do this by raising both sides of the equation to the power of4.(1x−84)4=24(\sqrt[4]{\frac{1}{} x-8})^4 =2^4(41​x−8​)4=24

STEP 3

implify both sides of the equation.\frac{1}{3} x-8 =2^

STEP 4

Calculate the value of 242^424.13x−8=16\frac{1}{3} x-8 =1631​x−8=16

STEP 5

Next, we need to isolate the term with xxx on one side of the equation. We can do this by adding8 to both sides of the equation.13x=16+8\frac{1}{3} x =16 +831​x=16+8

STEP 6

Calculate the value of 16+816 +816+8.13x=24\frac{1}{3} x =2431​x=24

STEP 7

Finally, to solve for xxx, we multiply both sides of the equation by3.x=24×3x =24 \times3x=24×3

STEP 8

Calculate the value of 24×324 \times324×3.x=72x =72x=72So, the solution to the equation 13x−84=2\sqrt[4]{\frac{1}{3} x-8}=2431​x−8​=2 is x=72x=72x=72.

Get Studdy

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: $\sqrt[4]{\frac{1}{3} x - 8} = 2$ . Choose one: a. $x=72$ , b. $x=8$ , c. $x=\frac{10}{3}$ , d. $x=-2$ .

Assumptions1. The equation is $\sqrt[4]{\frac{1}{3} x-8}=$ . We need to solve for $x$

First, we need to remove the fourth root from the equation. We can do this by raising both sides of the equation to the power of4.
$(\sqrt[4]{\frac{1}{} x-8})^4 =2^4$

implify both sides of the equation.
\frac{1}{3} x-8 =2^

Calculate the value of $2^4$ .
$\frac{1}{3} x-8 =16$

Next, we need to isolate the term with $x$ on one side of the equation. We can do this by adding8 to both sides of the equation.
$\frac{1}{3} x =16 +8$

Calculate the value of $16 +8$ .
$\frac{1}{3} x =24$

Finally, to solve for $x$ , we multiply both sides of the equation by3.
$x =24 \times3$

Calculate the value of $24 \times3$ .
$x =72$ So, the solution to the equation $\sqrt[4]{\frac{1}{3} x-8}=2$ is $x=72$ .