pieter wrote the equation (7h - 5(3h - 8) = -72) to model the number of hours it takes to dig a well to a level of 72 feet below sea level. how many hours will it take to dig the well?

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Question

pieter wrote the equation (7h - 5(3h - 8) = -72) to model the number of hours it takes to dig a well to a level of 72 feet below sea level. how many hours will it take to dig the well?

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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 Equations", "Distributive Property", "Combining Like Terms" ], "new_concepts": [], "current_concepts": [ "Linear Equations", "Distributive Property", "Combining Like Terms" ] } ## Apply the distributive property Using the *Distributive Property* knowledge point $$ \begin{aligned} &7h - 5(3h - 8) = -72 \ &7h - 15h + 40 = -72 \end{aligned} $$ ## Combine like terms Using the *Combining Like Terms* knowledge point $$ \begin{aligned} &(7 - 15)h + 40 = -72 \ &-8h + 40 = -72 \end{aligned} $$ ## Isolate the variable term Using the *Linear Equations* knowledge point $$ \begin{aligned} &-8h + 40 - 40 = -72 - 40 \ &-8h = -112 \end{aligned} $$ ## Solve for h Using the *Linear Equations* knowledge point $$ \begin{aligned} &h = \frac{-112}{-8} \ &h = 14 \end{aligned} $$

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

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QUESTION IMAGE

Question

Explanation:

Apply the distributive property

Combine like terms

Isolate the variable term

Solve for h

Answer: