$-3 \lt x \lt 1$ 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 $-3 \lt x \lt 1$