Answer
$(-∞,4)$
Work Step by Step
We are asked to solve $x-7\lt2$ and $2x+1\lt9$. Therefore, any solution of x must satisfy both inequalities.
First, we can solve $x-7\lt2$
Add 7 to both sides.
$x\lt9$
Next, we can solve $2x+1\lt9$
Subtract 1 from both sides.
$2x\lt8$
Divide both sides of the equation by 2.
$x\lt4$
Therefore, x is the set of numbers less than 4.