Lesson 1-6 – Compound Inequalities Compound Inequality

Lesson 1-6 – Compound Inequalities Compound Inequality – consists of two inequalities joined by the word and (conjunction) or the word or (disjunction). To solve an “and” compound inequality: Method 1 -- Solve each part of the inequality separately, then graph the solution set Method 2 -- Solve both parts at the same time making sure that you perform each operation to both sides of the individual inequalities then graph the solution set.

To graph the solution set on a number line: Graph the solution set for each inequality and find their intersection (area of overlap) The graph of an “and” compound inequality is called the intersection of the solution set of the two inequalities.

To solve an “or” compound inequality: Solve each inequality separately and then graph the solution set or

To graph the solution set on a number line: Graph each solution set separately and then combine on one number line The graph of an “or” compound inequality is the union of the solution set of the two inequalities.

Solving Absolute Value Inequalities Reminder: The absolute value of a number is its distance from 0 on the number line. It is always nonnegative.

To solve an absolute value inequality () or (≥) Using the definition of absolute value, graph the solution set on a number line Use the information on the graph to write out the solution set

Ex: *This means that all the values for

are at least

units or more from

on the number line.

Graph on a number line

The distance between

and

on the number line is greater than or equal to units

Now use this information to write out the solution set. or

In conclusion: Since

Is the same as

We can say that if:

or

then

or

then

or

Because the absolute value of a number is never negative: The solution of an inequality like is all real numbers The solution of an inequality like is the empty set

Solving a multistep absolute value inequality and graph the solution set.