Answer
All real numbers
Work Step by Step
We are given that $x-2\lt6$ or $3x+1\gt1$. Therefore, a solution only needs to satisfy one of the inequalities.
We can first solve $x-2\lt6$ for x.
Add 2 to both sides.
$x\lt8$
Next, can first solve $3x+1\gt1$ for x.
Subtract 1 from both sides.
$3x\gt0$
Divide both sides by 3.
$x\gt0$
Therefore, the solution set consists of all numbers that are either greater than 0 or less than 8, which includes all real numbers.