3.1.2 Solving Inequalities by Adding or Subtracting (continued) Example 2 Problem-Solving Application If the variable in an inequality represents something that cannot be measured as a decimal, such as number of books or people, then the solutions for that inequality will also be restricted to include only integer (or whole number) values. In this case, the graph of the inequality will show discrete points at those integer values, instead of a continuous shaded region.
Example 3 Money Application
Since inequalities can have an infinite number of solutions, it is not possible to check them all. However, the endpoints and the general direction of the inequality symbol can be checked. To check an endpoint, substitute the value of the endpoint into the related equation. The endpoint should be a solution to the equation. To check the direction of the inequality symbol, substitute any number from the solution region (other than the endpoint) into the inequality and confirm that it is a solution.
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