{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Equations", "Extraneous Solutions" ], "new_concepts": [], "current_concepts": [ "Radical Equations", "Extraneous Solutions" ] } ## Isolate the radical term \[ \begin{aligned} \sqrt{2x + 3} + 2 &= 7 \\ \sqrt{2x + 3} &= 5 \end{aligned} \] ## Square both sides to eliminate the radical \[ \begin{aligned} (\sqrt{2x + 3})^2 &= 5^2 \\ 2x + 3 &= 25 \end{aligned} \] ## Solve for x and verify the solution \[ \begin{aligned} 2x &= 22 \\ x &= 11 \end{aligned} \] Verification: \[ \sqrt{2(11) + 3} + 2 = \sqrt{25} + 2 = 5 + 2 = 7 \] $x = 11$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equations" ] }

\\\\sqrt{2x+3}+2=7\\

QUESTION IMAGE

$\\\\sqrt{2x+3}+2=7\\$

Question

\\\sqrt{2x+3}+2=7\\

Explanation:

Isolate the radical term

$$ LATEXBLOCK0 $$

Square both sides to eliminate the radical

$$ LATEXBLOCK1 $$

Solve for x and verify the solution

$$ LATEXBLOCK2 $$

Verification:

\sqrt{2(11) + 3} + 2 = \sqrt{25} + 2 = 5 + 2 = 7

Answer:

$x = 11$