2.6 compound inequalities quiz

write an inequality for graph 3:

graph 1
graph 2
graph 3
graph 4

\$x < -2\$ or \$x > 5\$
\$-2 \le x \le 5\$
\$-2 \le x < 5\$
\$x \le -2\$ or \$x > 5\$

Question

2.6 compound inequalities quiz write an inequality for graph 3: graph 1 graph 2 graph 3 graph 4 $x < -2$ or $x > 5$ $-2 \le x \le 5$ $-2 \le x < 5$ $x \le -2$ or $x > 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Compound Inequalities", "Graphing Inequalities" ], "new_concepts": [], "current_concepts": [ "Compound Inequalities", "Graphing Inequalities", "Union of Sets" ] } ## Analyze the boundary points of Graph 3 $$ \begin{aligned} &\text{Left boundary point: } x = -2 \quad (\text{solid circle, meaning } \le \text{ or } \ge) \ &\text{Right boundary point: } x = 5 \quad (\text{open circle, meaning } < \text{ or } >) \end{aligned} $$ ## Determine the shaded intervals $$ \begin{aligned} &\text{Left shaded region: } x \le -2 \ &\text{Right shaded region: } x > 5 \end{aligned} $$ ## Combine into a compound inequality $$ x \le -2 \text{ or } x > 5 $$

(A) $x < -2 \text{ or } x > 5$

(B) $-2 \le x \le 5$

(C) $-2 \le x < 5$

(D) $x \le -2 \text{ or } x > 5$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Compound Inequalities" ] }

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Question

Explanation:

Analyze the boundary points of Graph 3

Determine the shaded intervals

Combine into a compound inequality

Answer: