To solve this equation, we need to first combine like terms on both sides of the equation.
\( \frac{20}{15} + x + \frac{20}{14} - x = 3 \)
Simplify the fractions:
\( \frac{4}{3} + x + \frac{10}{7} - x = 3 \)
Now, combine the terms with x and the constant terms:
\( x - x + \frac{4}{3} + \frac{10}{7} = 3 \)
\( \frac{4}{3} + \frac{10}{7} = 3 \)
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 21:
\( \frac{28}{21} + \frac{30}{21} = 3 \)
\( \frac{58}{21} = 3 \)
Now, to solve for x:
\( x = 3 - \frac{58}{21} \)
\( x = \frac{63}{21} - \frac{58}{21} \)
\( x = \frac{5}{21} \)
Therefore, the solution to the equation is \( x = \frac{5}{21} \).
