Solved on Sep 15, 2023

Find the value of $x$ that satisfies the equation $\sqrt[3]{(1/8 - x)} = -1/2$ .

STEP 1

Assumptions1. The equation is $\sqrt[3]{\left(\frac{1}{8}-x\right)}=-\frac{1}{}$ . The solution is a real number

STEP 2

First, we need to remove the cube root from the equation. We can do this by cubing both sides of the equation.
\left(\sqrt[]{\left(\frac{1}{8}-x\right)}\right)^ = \left(-\frac{1}{2}\right)^

STEP 3

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

STEP 4

To isolate x, we need to move $\frac{1}{8}$ from the left side of the equation to the right side. We can do this by adding $\frac{1}{8}$ to both sides of the equation.
$-\frac{1}{8} + \frac{1}{8} - x = -\frac{1}{8} + \frac{1}{8}$

STEP 5

implify both sides of the equation.
$-x =0$

STEP 6

To solve for x, we need to multiply both sides of the equation by -1.
$-1 \times -x = -1 \times0$

STEP 7

implify both sides of the equation.
$x =0$ The solution is0.

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Find the value of $x$ that satisfies the equation $\sqrt[3]{(1/8 - x)} = -1/2$ .

STEP 1

Assumptions1. The equation is $\sqrt[3]{\left(\frac{1}{8}-x\right)}=-\frac{1}{}$ . The solution is a real number

STEP 2

First, we need to remove the cube root from the equation. We can do this by cubing both sides of the equation.
\left(\sqrt[]{\left(\frac{1}{8}-x\right)}\right)^ = \left(-\frac{1}{2}\right)^

STEP 3

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

STEP 4

To isolate x, we need to move $\frac{1}{8}$ from the left side of the equation to the right side. We can do this by adding $\frac{1}{8}$ to both sides of the equation.
$-\frac{1}{8} + \frac{1}{8} - x = -\frac{1}{8} + \frac{1}{8}$

STEP 5

implify both sides of the equation.
$-x =0$

STEP 6

To solve for x, we need to multiply both sides of the equation by -1.
$-1 \times -x = -1 \times0$

STEP 7

implify both sides of the equation.
$x =0$ The solution is0.

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Find the value of xxx that satisfies the equation (1/8−x)3=−1/2\sqrt[3]{(1/8 - x)} = -1/23(1/8−x)​=−1/2.

STEP 1

Assumptions1. The equation is (18−x)3=−1\sqrt[3]{\left(\frac{1}{8}-x\right)}=-\frac{1}{}3(81​−x)​=−1​ . The solution is a real number

STEP 2

First, we need to remove the cube root from the equation. We can do this by cubing both sides of the equation.\left(\sqrt[]{\left(\frac{1}{8}-x\right)}\right)^ = \left(-\frac{1}{2}\right)^

STEP 3

implify both sides of the equation.18−x=−18\frac{1}{8}-x = -\frac{1}{8}81​−x=−81​

STEP 4

To isolate x, we need to move 18\frac{1}{8}81​ from the left side of the equation to the right side. We can do this by adding 18\frac{1}{8}81​ to both sides of the equation.−18+18−x=−18+18-\frac{1}{8} + \frac{1}{8} - x = -\frac{1}{8} + \frac{1}{8}−81​+81​−x=−81​+81​

STEP 5

implify both sides of the equation.−x=0-x =0−x=0

STEP 6

To solve for x, we need to multiply both sides of the equation by -1.−1×−x=−1×0-1 \times -x = -1 \times0−1×−x=−1×0

STEP 7

implify both sides of the equation.x=0x =0x=0The solution is0.

Start learning now

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

Find the value of $x$ that satisfies the equation $\sqrt[3]{(1/8 - x)} = -1/2$ .

Assumptions1. The equation is $\sqrt[3]{\left(\frac{1}{8}-x\right)}=-\frac{1}{}$ . The solution is a real number

First, we need to remove the cube root from the equation. We can do this by cubing both sides of the equation.
\left(\sqrt[]{\left(\frac{1}{8}-x\right)}\right)^ = \left(-\frac{1}{2}\right)^

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

To isolate x, we need to move $\frac{1}{8}$ from the left side of the equation to the right side. We can do this by adding $\frac{1}{8}$ to both sides of the equation.
$-\frac{1}{8} + \frac{1}{8} - x = -\frac{1}{8} + \frac{1}{8}$

implify both sides of the equation.
$-x =0$

To solve for x, we need to multiply both sides of the equation by -1.
$-1 \times -x = -1 \times0$

implify both sides of the equation.
$x =0$ The solution is0.