\( -x-\frac{7}{5}=\frac{5}{2} x+\frac{2}{5} \) Simplify. your answer as much as possible \( x=\square \)

Let's solve the equation step-by-step. First, we want to get all the \( x \) terms on one side and the constant terms on the other side. The original equation is: \[ -x - \frac{7}{5} = \frac{5}{2} x + \frac{2}{5} \] Add \( x \) to both sides: \[ -\frac{7}{5} = \frac{5}{2} x + x + \frac{2}{5} \] Convert \( x \) to have a common denominator with \( \frac{5}{2} x \): \[ x = \frac{2}{2} x \Rightarrow \frac{5}{2} x + \frac{2}{2} x = \frac{7}{2} x \] Now the equation looks like this: \[ -\frac{7}{5} = \frac{7}{2} x + \frac{2}{5} \] Next, subtract \( \frac{2}{5} \) from both sides: \[ -\frac{7}{5} - \frac{2}{5} = \frac{7}{2} x \] Combine the fractions on the left: \[ -\frac{9}{5} = \frac{7}{2} x \] To isolate \( x \), multiply both sides by the reciprocal of \( \frac{7}{2} \), which is \( \frac{2}{7} \): \[ x = -\frac{9}{5} \cdot \frac{2}{7} = -\frac{18}{35} \] So your final simplified answer is: \[ x = -\frac{18}{35} \]