Question

solve: \\(\sqrt3{8x - 2} = 4\\)

to solve this equation, first dropdown both sides.

Explanation:

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<reasoning>

Identify the equation and operation

The given equation is:
\[\sqrt[3]{8x - 2} = 4\]
To eliminate the cube root on the left side, we need to apply the inverse operation of a cube root.

Apply exponent rules

Using the Exponent Rules knowledge point
\[

$$\begin{aligned} &(\sqrt[3]{a})^3 = a\\ &(\sqrt[3]{8x - 2})^3 = 4^3 \end{aligned}$$

\]

Simplify the equation

Using the Algebraic Simplification knowledge point
\[

$$\begin{aligned} &8x - 2 = 64\\ &8x = 66\\ &x = \frac{33}{4} \end{aligned}$$

\]
Thus, the first step to solve this radical equation is to cube both sides.
</reasoning>

<answer>
Solve: \(\sqrt[3]{8x - 2} = 4\)

To solve this equation, first <blank>cube</blank> both sides.
</answer>

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Answer:

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<reasoning>

Identify the equation and operation

The given equation is:
\[\sqrt[3]{8x - 2} = 4\]
To eliminate the cube root on the left side, we need to apply the inverse operation of a cube root.

Apply exponent rules

Using the Exponent Rules knowledge point
\[

$$\begin{aligned} &(\sqrt[3]{a})^3 = a\\ &(\sqrt[3]{8x - 2})^3 = 4^3 \end{aligned}$$

\]

Simplify the equation

Using the Algebraic Simplification knowledge point
\[

$$\begin{aligned} &8x - 2 = 64\\ &8x = 66\\ &x = \frac{33}{4} \end{aligned}$$

\]
Thus, the first step to solve this radical equation is to cube both sides.
</reasoning>

<answer>
Solve: \(\sqrt[3]{8x - 2} = 4\)

To solve this equation, first <blank>cube</blank> both sides.
</answer>

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