Answer:
x^2-2x-8<0
Explanation:
It is difficult visualizing the expressions, so lets change them to equations by substituting a "y" in place of the 0 of the inequality. This will allow us to graph the expressions. Then if we focus on only the y=0 line in the graph, we can find the correct inequality.
All four expressions are graphed with this substitution and included on the attached worksheet. Note the marked their marked differences. The two points on the given number line (-4,0) and (2,0) are marked on each graph.
What we should focus on first is which graphs actually intersect the two end values of x given on the number line: -4 and 2. Since we used y instead of "0" in the expressions, we are seeing everything, for all values of x. But what we really want are -4 and 2, which we can mark with (-4,0) and (2,0).
Only two graphs intersect (-4,0) and (2,0): the first and third (lower left). The first (x^2-2x-8<y) has the interior of the parabola colored blue - these are the valid points for the inequality. The number line between (-4,0) and (2,0) in included. The third (x^2-2x-8>y) is colored everywhere outside the parabola, and thus exclues the number line in the region we are interested. So the equation for this graph is not a valid possibility.
We may conclude that graph 1 is correct. The important section of the graph is expanded at the bottom. Since the graph line is dotted, the two points (-4,0) and (2,0) are not actually included on the line - they are simply a boundary, due to the < function. They would be included if the expression had said ≤ or ≥ (with the = sign).
The expression that represents the solution set is x^2-2x-8<0