$x + \frac{2}{5} = x - \frac{2}{3}$

Answer

This equation has no solution.

Explanation

x + \frac{2}{5} 15 x + 15 \cdot \frac{2}{5} 15 x + 6 15 x - 15 x 15 x - 15 x 0 = x - \frac{2}{3} = 15 x - 15 \cdot \frac{2}{3} = 15 x - 10 = - 10 - 6 = - 16 = - 16 multiply ALL terms by 15 . cancel out the denominators move the 15 x to the left side and 6 to the right simplify left and right hand side

Since the statement $0 = - 16$ is FALSE, we conclude that the equation has no solution.

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$x + \frac{2}{5} = x - \frac{2}{3}$