Write the solution set in interval notation, if it exists. \[ t-2<1 \text { or } 7 t-2<-1 \]

We begin with the inequality \[ t - 2 < 1 \text{ or } 7t - 2 < -1. \] **Step 1. Solve \(t - 2 < 1\):** Add \(2\) to both sides: \[ t < 1 + 2, \] so \[ t < 3. \] **Step 2. Solve \(7t - 2 < -1\):** Add \(2\) to both sides: \[ 7t < -1 + 2, \] so \[ 7t < 1. \] Now, divide both sides by \(7\): \[ t < \frac{1}{7}. \] **Step 3. Combine the two solutions using "or":** The solutions we found are: \[ t < 3 \quad \text{and} \quad t < \frac{1}{7}. \] Since \(t < \frac{1}{7}\) is a subset of \(t < 3\), the union of the two solution sets is simply: \[ t < 3. \] **Step 4. Express the result in interval notation:** The final solution set, in interval notation, is \[ (-\infty, 3). \]