solve for (w).

-\frac{1}{2} w - \frac{2}{3} = -\frac{1}{7}

simplify your answer as much as possible.

(w = \square)

Question

solve for (w).

-\frac{1}{2} w - \frac{2}{3} = -\frac{1}{7}

simplify your answer as much as possible.

(w = \square)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equation Solutions", "Solving for a Variable", "Fraction Addition", "Signed Fractions" ], "new_concepts": [], "current_concepts": [ "Linear Equation Solutions", "Solving for a Variable", "Fraction Addition", "Signed Fractions" ] } ## Isolate the variable term $$ \begin{aligned} -\frac{1}{2}w - \frac{2}{3} &= -\frac{1}{7} \ -\frac{1}{2}w &= -\frac{1}{7} + \frac{2}{3} \end{aligned} $$ ## Combine the fractions on the right side $$ \begin{aligned} -\frac{1}{2}w &= -\frac{3}{21} + \frac{14}{21} \ -\frac{1}{2}w &= \frac{11}{21} \end{aligned} $$ ## Solve for w $$ \begin{aligned} w &= \frac{11}{21} \cdot (-2) \ w &= -\frac{22}{21} \end{aligned} $$ Solve for $w$. $$-\frac{1}{2}w - \frac{2}{3} = -\frac{1}{7}$$ Simplify your answer as much as possible. $w =$ $-\frac{22}{21}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equation Solutions" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the variable term

Combine the fractions on the right side

Solve for w

Answer: