solve: $sqrt3{8x - 2}=4$. to solve this equation, first both sides.

Explanation:

Step1: Cube both sides

$$(\sqrt[3]{8x - 2})^3=4^3$$

Step2: Simplify the left - hand side

Since $(\sqrt[3]{a})^3=a$, the left - hand side becomes $8x - 2$, and the right - hand side is $64$. So we have the equation $8x-2 = 64$.

Step3: Add 2 to both sides

$8x-2 + 2=64 + 2$, which simplifies to $8x=66$.

Step4: Divide both sides by 8

$x=\frac{66}{8}=\frac{33}{4}$

Answer:

$x = \frac{33}{4}$