Solve the equation and check the solution. \( 10 \mathrm{t}=-26 \) The solution set is \( \{\square\} \). (Type an integer or a simplified fraction.)

1. The given equation is \[ 10t = -26. \] 2. To solve for \( t \), divide both sides by 10: \[ t = \frac{-26}{10}. \] 3. Simplify the fraction by dividing numerator and denominator by 2: \[ t = \frac{-13}{5}. \] 4. To check the solution, substitute \( t = \frac{-13}{5} \) back into the original equation: \[ 10\left(\frac{-13}{5}\right) = \frac{10 \times (-13)}{5} = \frac{-130}{5} = -26. \] Since the left-hand side equals the right-hand side, the solution is correct. The solution set is \( \left\{ -\frac{13}{5} \right\} \).