To solve the equation:
\[ \frac{2}{5}x + \frac{1}{5} = -\frac{9}{5} \]
we will follow these steps:
-
Isolate the term with \(x\).
Subtract \(\frac{1}{5}\) from both sides:
\[ \frac{2}{5}x = -\frac{9}{5} - \frac{1}{5} \]
Combine the fractions on the right side:
\[ -\frac{9}{5} - \frac{1}{5} = -\frac{10}{5} = -2 \]
So we have:
\[ \frac{2}{5}x = -2 \]
-
Solve for \(x\).
Multiply both sides by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\):
\[ x = -2 \times \frac{5}{2} \]
Simplifying this gives:
\[ x = -5 \]
Thus, the solution is:
\[ \boxed{-5} \]