type the correct answer in the box. use numerals instead of words.

what is the solution to this equation?

\\sqrt3{6x + 4} - 8 = -4\

the solution is $x =$ .

Question

type the correct answer in the box. use numerals instead of words.

what is the solution to this equation?

\\sqrt3{6x + 4} - 8 = -4\

the solution is $x =$  .

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Equations" ], "new_concepts": [], "current_concepts": [ "Radical Equations", "Algebraic Rearrangement" ] } ## Isolate the radical term $$ \begin{aligned} \sqrt[3]{6x + 4} - 8 &= -4 \ \sqrt[3]{6x + 4} &= -4 + 8 \ \sqrt[3]{6x + 4} &= 4 \end{aligned} $$ ## Cube both sides to eliminate the cube root $$ \begin{aligned} (\sqrt[3]{6x + 4})^3 &= 4^3 \ 6x + 4 &= 64 \end{aligned} $$ ## Solve for x $$ \begin{aligned} 6x &= 64 - 4 \ 6x &= 60 \ x &= 10 \end{aligned} $$ What is the solution to this equation? $$\sqrt[3]{6x + 4} - 8 = -4$$ The solution is $x =$ 10. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the radical term

Cube both sides to eliminate the cube root

Solve for x

Answer: