Solve the equation below, and check the solution. \( -\frac{3}{5} x=\frac{2}{5} \)

Let's solve the equation \( -\frac{3}{5} x = \frac{2}{5} \). To isolate \( x \), first divide both sides by \( -\frac{3}{5} \): \[ x = \frac{2/5}{-3/5} \] When dividing by a fraction, you can multiply by its reciprocal: \[ x = \frac{2}{5} \times \frac{5}{-3} = \frac{2 \times 5}{5 \times (-3)} = \frac{2}{-3} = -\frac{2}{3} \] Now, let's check the solution by substituting \( x \) back into the original equation: \[ -\frac{3}{5} \left( -\frac{2}{3} \right) = \frac{2}{5} \] The left side becomes: \[ \frac{3 \times 2}{5 \times 3} = \frac{6}{15} = \frac{2}{5} \] Since both sides of the equation are equal, the solution \( x = -\frac{2}{3} \) is confirmed to be correct!