To solve the equation \( \frac{12}{5}x + \frac{13}{20} = \frac{7}{20} \), we will begin by isolating the term involving \( x \).
- Start by subtracting \(\frac{13}{20}\) from both sides:
\[ \frac{12}{5}x = \frac{7}{20} - \frac{13}{20} \]
- Calculate the right side:
\[ \frac{12}{5}x = \frac{7 - 13}{20} = \frac{-6}{20} = -\frac{3}{10} \]
- Now, we have:
\[ \frac{12}{5}x = -\frac{3}{10} \]
- To isolate \( x \), multiply both sides by the reciprocal of \(\frac{12}{5}\), which is \(\frac{5}{12}\):
\[ x = -\frac{3}{10} \times \frac{5}{12} \]
- Multiply the fractions:
\[ x = -\frac{3 \times 5}{10 \times 12} = -\frac{15}{120} \]
- Simplify \(-\frac{15}{120}\):
\[ x = -\frac{1}{8} \]
Thus, the solution to the equation is:
\[ \boxed{-\frac{1}{8}} \]