You have learned how to use properties to solve inequalities and conjunctions of two inequalities. Solve the following problems. Click “Submit” when finished.

You have seen that the solution to the conjunction “<EQUATION> AND <EQUATION>” is the set of numbers that are both greater than <EQUATION> and less than <EQUATION>. Now, we will consider sentences such as “<EQUATION> OR <EQUATION>.” This type of sentence is called a |B| disjunction |/B| . A disjunction is true when one or both sentences are true. This means that the solution to the conjunction “<EQUATION> OR <EQUATION>” is the set of numbers that are less than <EQUATION>, greater than <EQUATION>, or both. The graph of the solution contains all numbers that are less than <EQUATION> and all numbers that are greater than <EQUATION>

We can write the solution using set notation.

Graph the disjunction “<EQUATION>.” Click “Submit” when finished.

We can use set notation to write the solution to “<EQUATION> or <EQUATION>”

Now, let’s graph the disjunction “<EQUATION> or <EQUATION>.” This disjunction is true when one or both sentences are true. This means that the solution is the set of numbers that are greater than <EQUATION> or greater than <EQUATION>.The graph of the solution contains all numbers that are greater than <EQUATION>.

Graph the disjunction “<EQUATION> or <EQUATION>.” To get only one circle on the number line, place both circles on top of each other. Click “Submit” when finished.

Consider the disjunction “<EQUATION> or <EQUATION>.” The solution set contains numbers that are greater than <EQUATION>, less than <EQUATION>, or both. But |I| all |/I| real numbers are greater than <EQUATION> or less than <EQUATION>. So the solution is the set of all real numbers and its graph is the entire number line.

Let’s solve the disjunction “<EQUATION> or <EQUATION>.” We solve each inequality separately. To solve the inequality on the left, add <EQUATION>” to each side. Then divide each side by <EQUATION>. Because we are dividing by a negative number, we must reverse the inequality symbol. So, we get <EQUATION>-4. To solve the inequality on the right, add <EQUATION> to each side. We get <EQUATION>. So the solution set is all numbers that are less than or equal to <EQUATION> or greater than <EQUATION>We can graph the solution set and describe it using set notation.

Solve the disjunction “<EQUATION>” and graph the solution set. Click “Submit” when finished.

We can write the solution using set notation.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education