Work Step by Step
We are given that $x-2\lt6$ and $3x+1\gt1$. Therefore, any solution for x must satisfy both inequalities. We can first solve $x-2\lt6$ for x. Add 2 to both sides. $x\lt8$ Next, we can 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 values of x that are greater than 0 and less than 8.