Answer
$(0,8)$
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.
