Answer
$(-1,4)$
See graph.
Work Step by Step
Step 1. Factor the inequality $x^2-3x\lt4\longrightarrow x^2-3x-4\lt0\longrightarrow (x+1)(x-4)\lt0$
Step 2. Identify the boundary points $x=-1,4$ for intervals formed $(-\infty,-1),(-1,4),(4,\infty)$
Step 3. Choose test values for each interval $x=-2,0,5$ and test the inequality to get $False,\ True,\ False$
Step 4. Thus we have the solution interval(s) $(-1,4)$
Step 5. See graph.
