Mrs. Agriesti's Algebra I Notes
6.4 Absolute Value and Inequalities
Objective:
To solve and graph compound inequalities.
Vocabulary:
- Absolute Value Inequality - an inequality that contains an absolute value.
- Conjunction - a compound inequality whose solution meets both conditions simultaneously.
- The solution can be written as a continuous statement such as a < x < b.
- It is an intersection or an 'and' set relationship.
- Disjunction - a compound inequality whose solution meets either of two separate statements.
- The solution is written as two separate statements such as x < a or x > b.
- It is a union or an 'or' set relationship.
Notes:
Solving
absolute value inequalities:
- Isolate the absolute value part (Get the absolute value part alone).
- Decide if the problem is a conjunction or a disjunction
- Conjunction - The form is like |x| < 7
- I call this a less and problem (almost rhymes with 'less than').
- Write this problem as a long conjoined problem −7 < x < 7
- Solve the problem like you would a normal inequality.
- Remember that you have three sides - what you do to one side you do to all.
- Disjunction - The form is like |x| > 7
- I call this a great or problem (almost rhymes with 'greater').
- Write this problem as two separate problems x > 7and x < −7
- Notice that the inequality symbol is switched and the sign is changed to negative on the second problem.
- Solve your rewritten inequality or inequalities.
Examples:
Solve:
Solve each inequality.
- |x + 9| > 13
- |3x − 15| < 12
- |10 − 4x| < 2
