solve: $5 |x - 6|

Question

solve: $5 |x - 6| < 4$

the answer has form:
$a < x < b$
$x < a$ or $x > b$

where $a =$
and $b =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Inequalities" ], "new_concepts": [], "current_concepts": [ "Absolute Value Inequalities", "Solving Inequalities" ] } ## Isolate the absolute value expression $$ \begin{aligned} 5|x - 6| &< 4 \ |x - 6| &< \frac{4}{5} \end{aligned} $$ ## Rewrite as a compound inequality $$ -\frac{4}{5} < x - 6 < \frac{4}{5} $$ ## Solve for x $$ \begin{aligned} 6 - \frac{4}{5} &< x < 6 + \frac{4}{5} \ \frac{26}{5} &< x < \frac{34}{5} \end{aligned} $$ The answer has form: $A < x < B$ $x < A \text{ or } x > B$ Where A = $\frac{26}{5}$ and B = $\frac{34}{5}$ { "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

Rewrite as a compound inequality

Solve for x

Answer: