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

what is the solution to this equation?

(7 - \sqrt3{2 - x} = 12)

the solution is (x = \square).

Question

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

what is the solution to this equation?

(7 - \sqrt3{2 - x} = 12)

the solution is (x = \square).

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", "Algebraic Rearrangement" ], "new_concepts": [], "current_concepts": [ "Radical Equations", "Algebraic Rearrangement" ] } ## Isolate the radical term $$ \begin{aligned} 7 - \sqrt[3]{2 - x} &= 12 \ -\sqrt[3]{2 - x} &= 5 \ \sqrt[3]{2 - x} &= -5 \end{aligned} $$ ## Cube both sides to eliminate the radical $$ \begin{aligned} 2 - x &= (-5)^3 \ 2 - x &= -125 \end{aligned} $$ ## Solve for x $$ \begin{aligned} -x &= -127 \ x &= 127 \end{aligned} $$ What is the solution to this equation? $7 - \sqrt[3]{2 - x} = 12$ The solution is $x =$ 127. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Isolate the radical term

Cube both sides to eliminate the radical

Solve for x

Answer: