question 2
in triangle $abc$, determine the possible values for $x$.

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Inequality Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Inequality Theorem", "Solving Inequalities" ] } ## Apply the triangle inequality theorem Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &|AB - AC| < BC < AB + AC \ &|15 - 3| < 2x - 4 < 15 + 3 \ &12 < 2x - 4 < 18 \end{aligned} $$ ## Solve the compound inequality $$ \begin{aligned} &12 + 4 < 2x < 18 + 4 \ &16 < 2x < 22 \ &8 < x < 11 \end{aligned} $$ $8 < x < 11$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Inequality Theorem" ] }

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Question

Explanation:

Apply the triangle inequality theorem

Solve the compound inequality

Answer: