09+Compound+'AND'+Inequalities

Section 6-4

 Compound Inequalities that contain the word "and" are true only if both inequalities are individually true. The graph of a compound inequality containing "and" is the intersection of the Inequalities graphs of the two inequalities that make up the compound inequality. To find the intersection, determine where the two graphs overlap .

__STEP1__: Separate the compound inequality into 2 inequalities (with an AND or OR) __STEP 2__: Solve each inequality completely and graph the solution. __STEP 3__: Put BOTH graphs on a single number line and write the answer as a compound inequality.

__Rules__ Rules to follow when solving inequalities

The first two rules are the same rules we use to solve equations:

1) We may add or subtract any quantity from both sides of the inequality and keep the same set of solutions to the inequality. 2) We may multiply or divide both sides of the inequality by any positive number and keep the same set of solutions.

The third rule is unique to inequalities 3) If we multiply or divide both sides of the inequality by a negative number, we need to reverse the direction of the inequality to keep the same solutions.

Let’s look at an example to see that the third rule is true. Consider the basic inequality. If we were to simply multiply both sides by -1, we would be left with, which is not true. By reversing the inequality sign, we get the true statement.



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