Answer
$-3 \lt x \lt 1$
Refer to the attached image below for the graph.
Work Step by Step
$x\lt1$ means all the real numbers less than (to the left of) $1$.
$x\gt-3$ means all the real numbers greater than (to the right of) $-3$.
(refer to the attached image below)
The conjunction used is AND, which means that both conditions/set must be satisfied. This means the solution set will contain the numbers that are common to both sets/intervals.
Note that the numbers common to both intervals are from -3 to 1 (but not including -3 and 1 themselves).
Thus, the solution to the compound inequality is $-3 \lt x \lt 1$
