5.5 solving systems of linear inequalities quiz

what inequality is graphed below?

$x \le 3$
$y \le 3$

Question

5.5 solving systems of linear inequalities quiz

what inequality is graphed below?

$x \le 3$
$y \le 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Inequalities", "Graphing Inequalities" ], "new_concepts": [], "current_concepts": [ "Linear Inequalities", "Graphing Inequalities" ] } ## Identify the boundary line Using the *Linear Inequalities* and *Graphing Inequalities* knowledge points $$ \begin{aligned} &\text{Boundary line is vertical: } x = c\ &\text{Line passes through } (3, 0)\ &\text{Equation of boundary: } x = 3\ &\text{Line style: solid (includes equality)} \end{aligned} $$ ## Determine the inequality sign Using the *Linear Inequalities* and *Graphing Inequalities* knowledge points $$ \begin{aligned} &\text{Shaded region is to the right of } x = 3\ &\text{Test point } (5, 0): 5 \ge 3 \quad (\text{True})\ &\text{Inequality: } x \ge 3 \end{aligned} $$ ## Match with the given options Using the *Linear Inequalities* knowledge point $$ \begin{aligned} &\text{Option 1: } x \le 3 \quad (\text{Incorrect})\ &\text{Option 2: } y \le 3 \quad (\text{Incorrect})\ &\text{Correct inequality: } x \ge 3 \end{aligned} $$

(A) $x \le 3$

(B) $y \le 3$

(C) $x \ge 3$

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

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QUESTION IMAGE

Question

Explanation:

Identify the boundary line

Determine the inequality sign

Match with the given options

Answer: