QuestionWhich equation shows a valid step in solving $\sqrt[3]{2 x-6}+\sqrt[3]{2 x+6}=0$ ? $(\sqrt[3]{2 x-6})^{2}=(\sqrt[3]{2 x+6})^{2}$ $(\sqrt[3]{2 x-6})^{2}=(-\sqrt[3]{2 x+6})^{2}$ $(\sqrt[3]{2 x-6})^{3}=(\sqrt[3]{2 x+6})^{3}$ $(\sqrt[3]{2 x-6})^{3}=(-\sqrt[3]{2 x+6})^{3}$ Mark this and return sessmentViewer/Activit...

Studdy Solution

STEP 1

1. We are given the equation $\sqrt[3]{2x-6} + \sqrt[3]{2x+6} = 0$ .
2. We need to find a valid algebraic step in solving this equation.

STEP 2

1. Understand the given equation.
2. Simplify the equation to find a valid step.
3. Identify the correct algebraic transformation.

STEP 3

The equation $\sqrt[3]{2x-6} + \sqrt[3]{2x+6} = 0$ implies that the sum of two cube roots is zero.

STEP 4

If the sum of two cube roots is zero, then they must be negatives of each other. Therefore, we have: $\sqrt[3]{2x-6} = -\sqrt[3]{2x+6}$

STEP 5

To eliminate the cube roots, we cube both sides of the equation: $(\sqrt[3]{2x-6})^3 = (-\sqrt[3]{2x+6})^3$
The valid algebraic step is:
\[ (\sqrt[3]{2x-6})^3 = (-\sqrt[3]{2x+6})^3 $

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