Learning Resources

Investigation 5:Square-Root Functions and Discontinuities

Step B:

The inequality (x + 2)(x - 3) 0 is more difficult to solve than the previous inequality. Two approaches are possible.

1. Clearly, -2 and 3 are the key points. Placing them on a sign graph will divide the x-axis into three intervals. A sign check will indicate the intervals that satisfy the inequality.
2. If the product of two expressions is greater than or equal to zero, then logically, either the expressions are both greater than or equal to zero, or they are both less than or equal to zero. This stems from the fact that to ensure a positive product from two numbers, they must be both positive or both negative. Hence, solving the following inequalities will produce the correct solution.
   (x + 2) > 0 and (x - 3) > 0      OR      (x + 2) < 0 and (x - 3) < 0