text: ## Thinking Mathematically (6th Edition)
  
  We start with the original equation: $\frac{y}{3}$ + $\frac{2}{5}$ = $\frac{y}{5}$ - $\frac{2}{5}$ We can start by finding the least common denominator for all of the fractions. The least common denominator is 15. We can now write all of the fractions as equivalents with a denominator of 15. This gives us: $\frac{5y}{15}$ + $\frac{6}{15}$ = $\frac{3y}{15}$ - $\frac{6}{15}$ We can now subtract $\frac{3y}{15}$ from both sides of the equation. $\frac{5y}{15}$ - $\frac{3y}{15}$ + $\frac{6}{15}$ = $\frac{3y}{15}$ - $\frac{3y}{15}$ - $\frac{6}{15}$ Completing the arithmetic, we get: $\frac{2y}{15}$ + $\frac{6}{15}$ = -$\frac{6}{15}$ Next, subtract $\frac{6}{15}$ from both sides of the equation. $\frac{2y}{15}$ + $\frac{6}{15}$ - $\frac{6}{15}$ = -$\frac{6}{15}$ - $\frac{6}{15}$ Complete the arithmetic: $\frac{2y}{15}$ = $\frac{-12}{15}$ Now, cross multiply so that: 2y(15) = (-12)(15) And, 30y = -180 Last, divide both sides by 30. $\frac{30y}{30}$ = $\frac{-180}{30}$ Complete the division and get y = -6. We can check by substituting -6 back into the original equations for y. $\frac{-6}{3}$ + $\frac{2}{5}$ = $\frac{-6}{5}$ - $\frac{2}{5}$ Now, complete the arithmetic on each side of the equation. -2 + $\frac{2}{5}$ = $\frac{-8}{5}$ $\frac{-10}{5}$ + $\frac{2}{5}$ = $\frac{-8}{5}$ In the step above, we rewrote -2 as a fraction using a denominator of 5. We get $\frac{-8}{5}$ = $\frac{-8}{5}$ Showing that our solution of y = -6 is correct.
explanation: The document contains a detailed step-by-step solution to a math problem, specifically solving the equation \(\frac{y}{3} + \frac{2}{5} = \frac{y}{5} - \frac{2}{5}\). The solution is provided, and the final answer is \(y = -6\). The document also includes a verification step to confirm the solution.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## Thinking Mathematically (6th Edition)
  
  We start with the original equation: $\frac{y}{3}$ + $\frac{2}{5}$ = $\frac{y}{5}$ - $\frac{2}{5}$ We can start by finding the least common denominator for all of the fractions. The least common denominator is 15. We can now write all of the fractions as equivalents with a denominator of 15. This gives us: $\frac{5y}{15}$ + $\frac{6}{15}$ = $\frac{3y}{15}$ - $\frac{6}{15}$ We can now subtract $\frac{3y}{15}$ from both sides of the equation. $\frac{5y}{15}$ - $\frac{3y}{15}$ + $\frac{6}{15}$ = $\frac{3y}{15}$ - $\frac{3y}{15}$ - $\frac{6}{15}$ Completing the arithmetic, we get: $\frac{2y}{15}$ + $\frac{6}{15}$ = -$\frac{6}{15}$ Next, subtract $\frac{6}{15}$ from both sides of the equation. $\frac{2y}{15}$ + $\frac{6}{15}$ - $\frac{6}{15}$ = -$\frac{6}{15}$ - $\frac{6}{15}$ Complete the arithmetic: $\frac{2y}{15}$ = $\frac{-12}{15}$ Now, cross multiply so that: 2y(15) = (-12)(15) And, 30y = -180 Last, divide both sides by 30. $\frac{30y}{30}$ = $\frac{-180}{30}$ Complete the division and get y = -6. We can check by substituting -6 back into the original equations for y. $\frac{-6}{3}$ + $\frac{2}{5}$ = $\frac{-6}{5}$ - $\frac{2}{5}$ Now, complete the arithmetic on each side of the equation. -2 + $\frac{2}{5}$ = $\frac{-8}{5}$ $\frac{-10}{5}$ + $\frac{2}{5}$ = $\frac{-8}{5}$ In the step above, we rewrote -2 as a fraction using a denominator of 5. We get $\frac{-8}{5}$ = $\frac{-8}{5}$ Showing that our solution of y = -6 is correct.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a detailed step-by-step solution to a math problem, specifically solving the equation \(\frac{y}{3} + \frac{2}{5} = \frac{y}{5} - \frac{2}{5}\). The solution is provided, and the final answer is \(y = -6\). The document also includes a verification step to confirm the solution.
  
  Label: question-and-answer