a larger number is double the sum of 3 and a smaller number. the larger number is 2 less than 3 times the smaller number. if y represents the larger number and x represents the smaller number, which equations model the situation? check all that apply.

$y = 3x - 2$

$3x - y = 2$

$3x - y = -2$

$y = 2 - 3x$

$y = 2(x + 3)$

Question

a larger number is double the sum of 3 and a smaller number. the larger number is 2 less than 3 times the smaller number. if y represents the larger number and x represents the smaller number, which equations model the situation? check all that apply.

\$y = 3x - 2\$

\$3x - y = 2\$

\$3x - y = -2\$

\$y = 2 - 3x\$

\$y = 2(x + 3)\$

$y = 3x - 2$

$3x - y = 2$

$3x - y = -2$

$y = 2 - 3x$

$y = 2(x + 3)$

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": [ "Variable Identification", "Algebraic Translation", "System of Equations Translation" ], "new_concepts": [], "current_concepts": [ "Variable Identification", "Algebraic Translation", "System of Equations Translation" ] } ## Identify the variables Using the *Variable Identification* knowledge point $$ \begin{aligned} &y = \text{larger number}\ &x = \text{smaller number} \end{aligned} $$ ## Translate the first sentence Using the *Algebraic Translation* knowledge point $$ \begin{aligned} &\text{"A larger number is double the sum of 3 and a smaller number"}\ &y = 2(3 + x)\ &y = 2(x + 3) \end{aligned} $$ ## Translate the second sentence Using the *Algebraic Translation* knowledge point $$ \begin{aligned} &\text{"The larger number is 2 less than 3 times the smaller number"}\ &y = 3x - 2 \end{aligned} $$ ## Rearrange the second equation Using the *System of Equations Translation* knowledge point $$ \begin{aligned} &y = 3x - 2\ &3x - y = 2 \end{aligned} $$ ## Match with the given options Using the *System of Equations Translation* knowledge point $$ \begin{aligned} &\text{Matching equations:}\ &y = 3x - 2 \quad (\text{Option 1})\ &3x - y = 2 \quad (\text{Option 2})\ &y = 2(x + 3) \quad (\text{Option 5}) \end{aligned} $$

(A) $y = 3x - 2$

(B) $3x - y = 2$

(C) $3x - y = -2$

(D) $y = 2 - 3x$

(E) $y = 2(x + 3)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "System of Equations Translation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the variables

Translate the first sentence

Translate the second sentence

Rearrange the second equation

Match with the given options

Answer: