question 10 · 1 point

solve $|3x - 3| + 9

Question

question 10 · 1 point

solve $|3x - 3| + 9 < 8$ and write the solution in interval notation.

(if there is no solution, enter your answer as $\varnothing$.)

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Inequalities", "No Solution Equations" ], "new_concepts": [], "current_concepts": [ "Absolute Value Inequalities", "No Solution Equations", "Interval Notation" ] } ## Isolate the absolute value expression Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} |3x - 3| + 9 &< 8 \ |3x - 3| &< 8 - 9 \ |3x - 3| &< -1 \end{aligned} $$ ## Analyze the inequality for solutions Using the *No Solution Equations* and *Absolute Value Inequalities* knowledge points $$ \begin{aligned} &\text{Since } |3x - 3| \ge 0 \text{ for all real numbers } x,\ &\text{the inequality } |3x - 3| < -1 \text{ has no solution.} \end{aligned} $$ Solve $|3x - 3| + 9 < 8$ and write the solution in interval notation. (If there is no solution, enter your answer as $\varnothing$.) Provide your answer below: $\varnothing$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the absolute value expression

Analyze the inequality for solutions

Answer: