SOLUTION: Need help solving this inequality. (x+5)(x-1)(x+3)>0

Question 184081: Need help solving this inequality. (x+5)(x-1)(x+3)>0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Change the inequality sign to an equals sign, then solve using the Zero Product Rule. That will give you three critical points, namely:

Now specify 4 intervals based on those critical points:

Note that the interval specifications do not include the endpoints (they are specified with parentheses rather than square brackets). That is because equality was not included in your original inequality symbol, i.e. it was

rather than

Next, select one value from each of the intervals that does not include an interval endpoint. For example, from

you could pick 0 or -1, but do not select -3 or 1.

For each of the four selected values, substitute the value back into the original inequality. Two of the values should make the inequality true, and two of them will make the inequality false.

The union of the two intervals that contain the values that gave you a true result is the solution set of your inequality.

As a check on your work, compare your answers to the regions where the graph shown is above the x-axis, i.e. f(x)>0

John

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