#6. solve the radical equations:
a) $\sqrt{3x - 2} = 7$

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Radical Equations", "Solving Radical Equations" ], "current_concepts": [ "Radical Equations", "Solving Radical Equations" ] } ## Isolate the radical and square both sides $$ \begin{aligned} \sqrt{3x - 2} &= 7 \ (\sqrt{3x - 2})^2 &= 7^2 \ 3x - 2 &= 49 \end{aligned} $$ ## Solve for x $$ \begin{aligned} 3x &= 49 + 2 \ 3x &= 51 \ x &= 17 \end{aligned} $$ ## Verify the solution $$ \begin{aligned} \text{LHS} &= \sqrt{3(17) - 2} = \sqrt{51 - 2} = \sqrt{49} = 7 \ \text{RHS} &= 7 \ \text{LHS} &= \text{RHS} \end{aligned} $$ Solve the radical equation: a) $\sqrt{3x - 2} = 7$ is $x = 17$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equations" ] }

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Question

Explanation:

Isolate the radical and square both sides

Solve for x

Verify the solution

Answer: