Absolute Value Inequalities
When solving an absolute value equation or inequality, understand that the value of the inside of the absolute value symbol may be positive or negative ... once the absolute value is evaluated the result is always positive. In other words, or .
Absolute value inequalities are solved in a similar fashion as absolute value equations. Understand that the less than and less than or equal to inequalities are compound statements.
would mean that the value for
between the values of 5 and 5. Therefore, you would set up a compound inequality
to solve the problem.
Solving this compound inequality would provide the result that . Which means that the value for x lies between 1 and 4.
(graph) [ ]
(interval notation) notice that this is an Intersection of two sets of numbers.
The greater than and greater than or equal to inequalities are disjoint statements. This means that you must disjoin them or take them apart to solve. The answer to the inequality will be greater than the positive value of the number or less than the negative value of the number. The answer is the union of the two inequalities.
Solve the inequality: . This would mean that the value for would be greater than 5 or the value for would be less than 5. When you disjoin the inequality to solve, the problem would look like this: or
Solving these inequalities would provide the result or .
(graph) ) (
(interval notation) notice that this is a Union of two sets of numbers.
The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was
The views and
opinions expressed in this page are strictly those of Mary Lou Baker.
This page was edited on 09-Jan-2014