To solve the equation \( x - 1 \frac{2}{5} = 6 \frac{1}{10} \), we can first convert the mixed numbers into improper fractions.
-
Convert \( 1 \frac{2}{5} \): \[ 1 \frac{2}{5} = 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5} \]
-
Convert \( 6 \frac{1}{10} \): \[ 6 \frac{1}{10} = 6 + \frac{1}{10} = \frac{60}{10} + \frac{1}{10} = \frac{61}{10} \]
Now, replace the mixed numbers in the equation: \[ x - \frac{7}{5} = \frac{61}{10} \]
Next, add \( \frac{7}{5} \) to both sides: \[ x = \frac{61}{10} + \frac{7}{5} \]
To add these fractions, we need a common denominator. The least common multiple of 10 and 5 is 10. Convert \( \frac{7}{5} \) to have a denominator of 10: \[ \frac{7}{5} = \frac{7 \times 2}{5 \times 2} = \frac{14}{10} \]
Now, add the fractions: \[ x = \frac{61}{10} + \frac{14}{10} = \frac{61 + 14}{10} = \frac{75}{10} \]
Simplifying \( \frac{75}{10} \): \[ x = \frac{75 \div 5}{10 \div 5} = \frac{15}{2} = 7 \frac{1}{2} \]
Thus, the solution is: \[ \boxed{7 \frac{1}{2}} \]