How Are Inequalities Solved and Solutions Graphed?

Solving inequalities and graphing solutions is accomplished through a multi-step process that begins with using inverse operations to solve the inequality, then placing the solution sets on a graph. Inequalities may be solved in the same manner used to solve equations. This involves using an opposite operation to balance out the equation, which might involve addition, subtraction, multiplication or division.

Even though inverse operations are used to solve the equation, the inequality symbol remains the same. Once the equation has been solved, only the inequality symbol and remaining value should be left. The value will be noted as either less than or greater than N. The inequality might read, for instance, as N is less than or equal to (the value of) 5. That means the solutions created by the inequality include the value 5 and all numbers less than 5. On a graph, that solution is drawn by creating a number line, such as from zero to ten, then highlighting all numbers up to and including five, starting at zero. The solution may include negative numbers less than zero, which can be demonstrated on the graph by stopping at the number zero, then drawing an arrow to indicate the solutions go beyond that point.