the point $(0, 0)$ is a solution to which of these inequalities?

a. $y + 7

Question

the point $(0, 0)$ is a solution to which of these inequalities?

a. $y + 7 < 2x + 6$
b. $y - 7 < 2x - 6$
c. $y - 6 < 2x - 7$
d. $y + 7 < 2x - 6$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Evaluating Inequalities" ], "current_concepts": [ "Evaluating Inequalities", "Linear Inequalities" ] } ## Substitute point into Option A $$ \begin{aligned} y + 7 &< 2x + 6 \ 0 + 7 &< 2(0) + 6 \ 7 &< 6 \quad (\text{False}) \end{aligned} $$ ## Substitute point into Option B $$ \begin{aligned} y - 7 &< 2x - 6 \ 0 - 7 &< 2(0) - 6 \ -7 &< -6 \quad (\text{True}) \end{aligned} $$ ## Substitute point into Options C and D $$ \begin{aligned} \text{Option C: } 0 - 6 &< 2(0) - 7 \implies -6 < -7 \quad (\text{False}) \ \text{Option D: } 0 + 7 &< 2(0) - 6 \implies 7 < -6 \quad (\text{False}) \end{aligned} $$

A. $y+7 < 2x+6$

B. $y-7 < 2x-6$

C. $y-6 < 2x-7$

D. $y+7 < 2x-6$

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

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QUESTION IMAGE

Question

Explanation:

Substitute point into Option A

Substitute point into Option B

Substitute point into Options C and D

Answer: