Question

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

to solve this equation, first cube both sides.

\\(x = \\)
8.25
0.75
1.75
2.25
no real solutions

Explanation:

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<reasoning>

Cube both sides of the equation

Using the Cube Root Equations knowledge point
\[

$$\begin{aligned} \sqrt[3]{8x - 2} &= 4 \\ (\sqrt[3]{8x - 2})^3 &= 4^3 \\ 8x - 2 &= 64 \end{aligned}$$

\]

Solve the linear equation for x

Using the Solving Radical Equations knowledge point
\[

$$\begin{aligned} 8x &= 64 + 2 \\ 8x &= 66 \\ x &= \frac{66}{8} \\ x &= 8.25 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

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

Question 2

<mcq-correct>(A) 8.25</mcq-correct>
<mcq-option>(B) 0.75</mcq-option>
<mcq-option>(C) 1.75</mcq-option>
<mcq-option>(D) 2.25</mcq-option>
<mcq-option>(E) no real solutions</mcq-option>
</answer>

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Answer:

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<reasoning>

Cube both sides of the equation

Using the Cube Root Equations knowledge point
\[

$$\begin{aligned} \sqrt[3]{8x - 2} &= 4 \\ (\sqrt[3]{8x - 2})^3 &= 4^3 \\ 8x - 2 &= 64 \end{aligned}$$

\]

Solve the linear equation for x

Using the Solving Radical Equations knowledge point
\[

$$\begin{aligned} 8x &= 64 + 2 \\ 8x &= 66 \\ x &= \frac{66}{8} \\ x &= 8.25 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

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

Question 2

<mcq-correct>(A) 8.25</mcq-correct>
<mcq-option>(B) 0.75</mcq-option>
<mcq-option>(C) 1.75</mcq-option>
<mcq-option>(D) 2.25</mcq-option>
<mcq-option>(E) no real solutions</mcq-option>
</answer>

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