solve for (w).

\2(w - 6) - 7 = -3(-8w + 5) - 4w\

simplify your answer as much as possible.

Question

solve for (w).

\2(w - 6) - 7 = -3(-8w + 5) - 4w\

simplify your answer as much as possible.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Equations", "Algebraic Simplification", "Solving for a Variable" ], "new_concepts": [], "current_concepts": [ "Linear Equations", "Algebraic Simplification", "Solving for a Variable" ] } ## Apply the distributive property Using the *Algebraic Simplification* knowledge point $$ \begin{aligned} 2(w - 6) - 7 &= -3(-8w + 5) - 4w \ 2w - 12 - 7 &= 24w - 15 - 4w \end{aligned} $$ ## Combine like terms on both sides Using the *Algebraic Simplification* knowledge point $$ \begin{aligned} 2w - 19 &= (24w - 4w) - 15 \ 2w - 19 &= 20w - 15 \end{aligned} $$ ## Isolate the variable terms Using the *Solving for a Variable* and *Linear Equations* knowledge points $$ \begin{aligned} 2w - 20w &= -15 + 19 \ -18w &= 4 \end{aligned} $$ ## Solve for w Using the *Solving for a Variable* and *Linear Equations* knowledge points $$ \begin{aligned} w &= \frac{4}{-18} \ w &= -\frac{2}{9} \end{aligned} $$ $w = -\frac{2}{9}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the distributive property

Combine like terms on both sides

Isolate the variable terms

Solve for w

Answer: