solve: (5|x+4|+3 7) the answer has form: $a

Question

solve: (5|x+4|+3 > 7) 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", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Absolute Value Inequalities" ], "new_concepts": [], "current_concepts": [ "Absolute Value Inequalities", "Solving Inequalities" ] } ## Isolate the absolute value expression Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} 5|x + 4| + 3 &> 7 \ 5|x + 4| &> 4 \ |x + 4| &> \frac{4}{5} \end{aligned} $$ ## Split into two separate inequalities Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} x + 4 < -\frac{4}{5} \quad &\text{or} \quad x + 4 > \frac{4}{5} \end{aligned} $$ ## Solve each inequality for x Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} x < -4 - \frac{4}{5} \quad &\text{or} \quad x > -4 + \frac{4}{5} \ x < -\frac{24}{5} \quad &\text{or} \quad x > -\frac{16}{5} \end{aligned} $$ ## Identify the form and values of A and B Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} &\text{Form: } x < A \text{ or } x > B \ &A = -\frac{24}{5} \ &B = -\frac{16}{5} \end{aligned} $$ The answer has form: $A < x < B$ $x < A \text{ or } x > B$ Where $A =$ $-\frac{24}{5}$ and $B =$ $-\frac{16}{5}$ { "elements": [ { "type": "bentinequality", "params": [{ "x": -4.8, "operator": "<", "labelText": "x < -\frac{24}{5}" }], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "showLabel": true } }, { "type": "bentinequality", "params": [{ "x": -3.2, "operator": ">", "labelText": "x > -\frac{16}{5}" }], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "showLabel": true } }, { "type": "point", "params": [[-4.8, 0]], "properties": { "name": "A", "size": 4, "color": "#F2557F", "fillColor": "white", "strokeColor": "#F2557F", "withLabel": false } }, { "type": "point", "params": [[-3.2, 0]], "properties": { "name": "B", "size": 4, "color": "#F2557F", "fillColor": "white", "strokeColor": "#F2557F", "withLabel": false } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Inequalities" ] }

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Question

Explanation:

Isolate the absolute value expression

Split into two separate inequalities

Solve each inequality for x

Identify the form and values of A and B

Answer: