$$x+\frac{2}{5} = x-\frac{2}{3}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x+\frac{2}{5} &= x-\frac{2}{3}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15x+15\cdot\frac{2}{5} &= 15x-15\cdot\frac{2}{3}&& \text{cancel out the denominators} \\[1 em]15x+6 &= 15x-10&& \text{move the $ \color{blue}{ 15x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]15x-15x &= -10-6&& \text{simplify left and right hand side} \\[1 em]15x-15x &= -16&& \\[1 em]0 &= -16&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -16 } $ is FALSE, we conclude that the equation has no solution.
This page was created using
Equations Solver