Question
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b. \( \frac{1}{7}-\square=-\frac{1}{14} \)

Ask by French Chavez. in Argentina
Mar 17,2025

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Tutor-Verified Answer

Answer

La solución es \( \frac{3}{14} \).

Solution

1. Planteamos la ecuación: \[ \frac{1}{7} - x = -\frac{1}{14} \] 2. Restamos \(\frac{1}{7}\) a ambos lados para aislar \(-x\): \[ -x = -\frac{1}{14} - \frac{1}{7} \] 3. Convertimos \(\frac{1}{7}\) a denominador 14: \[ \frac{1}{7} = \frac{2}{14} \] 4. Realizamos la suma: \[ -x = -\frac{1}{14} - \frac{2}{14} = -\frac{3}{14} \] 5. Multiplicamos ambos lados por \(-1\) para despejar \(x\): \[ x = \frac{3}{14} \] La solución es: \[ \frac{3}{14} \]

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The Deep Dive

To solve the equation \( \frac{1}{7} - \square = -\frac{1}{14} \), you can start by isolating the square. Add \(\square\) to both sides and move \(-\frac{1}{14}\) to the left side, yielding: \(\square = \frac{1}{7} + \frac{1}{14}\). To add these fractions, find a common denominator, which is 14. Rewrite \(\frac{1}{7}\) as \(\frac{2}{14}\), then combine: \(\square = \frac{2}{14} + \frac{1}{14} = \frac{3}{14}\). So, \( \square = \frac{3}{14} \). Now, if you're curious about the connections behind these fractions, the key lies in understanding how to manipulate common denominators seamlessly! Fractions can sometimes feel tricky, but they’re just fun puzzles waiting to be solved. Understanding real-world applications of fractions is fantastic too! Whether you’re cooking and need to adjust a recipe or cutting a pizza for your friends, knowing how to handle fractions is crucial. Mastering this skill turns fraction confusion into culinary triumphs or jubilant feasts!

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