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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Equations" ], "new_concepts": [], "current_concepts": [ "Radical Equations", "Extraneous Solutions" ] } ## Isolate the radical and square both sides $$ \begin{aligned} \sqrt{x - 4} &= 3 \ (\sqrt{x - 4})^2 &= 3^2 \ x - 4 &= 9 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x &= 9 + 4 \ x &= 13 \end{aligned} $$ ## Check for extraneous solutions $$ \begin{aligned} \text{Substitute } x = 13 \text{ into } \sqrt{x - 4} &= 3: \ \sqrt{13 - 4} &= \sqrt{9} = 3 \quad (\text{True}) \end{aligned} $$ Since $x = 13$ is the correct solution, and it is not listed among the options (8, 16, 85), the correct choice is "no solution".

(A) 8

(B) 16

(C) 85

(D) no solution

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the radical and square both sides

Solve for x

Check for extraneous solutions

Answer: