. \( x+\frac{1}{5}=\frac{2}{3} \)

To solve the equation \( x + \frac{1}{5} = \frac{2}{3} \), start by isolating \( x \). You can do this by subtracting \( \frac{1}{5} \) from both sides. This leads to: \[ x = \frac{2}{3} - \frac{1}{5}. \] Now, to perform the subtraction, find a common denominator. The least common multiple of 3 and 5 is 15. Rewrite the fractions: \[ \frac{2}{3} = \frac{10}{15} \quad \text{and} \quad \frac{1}{5} = \frac{3}{15}. \] Now substitute these values back in: \[ x = \frac{10}{15} - \frac{3}{15} = \frac{7}{15}. \] Therefore, \( x = \frac{7}{15} \). --- Did you know that algebra traces its roots back over a thousand years to ancient civilizations? The Arabs, especially, played a crucial role in its development during the Middle Ages, with scholars like Al-Khwarizmi paving the way for equations just like the one you just solved! If you ever find yourself stuck on a problem like this, remember to double-check your common denominators and fractions! Many people trip up by forgetting to convert both fractions to an equivalent base before subtracting. With a little practice, it'll become second nature!