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

to solve this equation, first dropdown both sides.

Question

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

to solve this equation, first dropdown both sides.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Algebraic Simplification" ], "new_concepts": [ "Solving Radical Equations", "Cube Root Equations" ], "current_concepts": [ "Exponent Rules", "Algebraic Simplification", "Solving Radical Equations", "Cube Root Equations" ] } ## 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. Solve: $\sqrt[3]{8x - 2} = 4$ To solve this equation, first cube both sides. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Radical Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the equation and operation

Apply exponent rules

Simplify the equation

Answer: