The solution will be all points that are more than two units away from zero.">
For details on it including licensingclick here. This book is licensed under a Creative Commons by-nc-sa 3. See the license for more details, but that basically means you can share this book as long as you credit the author but see belowdon't make money from it, and do make it available to everyone else under the same terms. This content was accessible as of December 29,and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book.
Please tell us who you are Please start by selecting all of the fields. If you are under 18, we require the consent of a parent or guardian before creating your account. Their email address will be used to request their consent.
To access sofatutor content, please agree our Terms and Conditions and the Privacy Statement. In biology class, Daisy learned that the average human body temperature is How can she calculate a temperature that will make her appear to be too sick to go to school?
So the average body temperature is The x - Let's see what that would look like: Notice how the absolute value bars are removed. Now to solve Daisy's problem. It's easier to calculate this problem if we write it as two inequalities: Now solve by isolating the variable.
There are two expressions: So, in plain English, this means that a temperature as low as You can write the solution to this absolute value inequality in several ways.
You can write it as two inequalities joined by the word 'and,' or like this using the less than operator.
The solution set is all the numbers between Inclusive is equivalent to drawing a closed circle on a number line. Notice how the inequality is displayed on the thermometer. The healthy zone is shown on one section of the thermometer.
Let's write the inequality for the danger zone.
When you have an equation containing the greater than sign and the absolute value is on the left side of the equation, the solution should be written with two statements that can be joined by the word OR.
Notice the absolute value bars are gone. Ok let's help Daisy figure out how to solve this problem. Use the format to write two inequalities. The solution for the x - Notice how the solution set is displayed on the thermometer.
You have closed circles at With an or situation, the solution set is always divided into two pieces. Okay, lets put all this information together so Daisy can figure out what temperature will make her appear too sick to go to school.
The healthy zone is greater than or equal to The danger zone is less than or equal to Luckily, Daisy knows just the right place to get the perfect thermometer reading Scroll Up About this Video Lesson Description Absolute value inequalities can include variable expressions inside the absolute value bars.
Similar to absolute value equations with a variable expression inside the absolute value bars, you must set up a positive and negative situation, but look out because inequalities behave differently depending if they are less than or greater than situations also less than and equal to or greater than and equal to.
For less than situations, an AND situation is created. Solve for both, and graph the two solutions on a number line; the solution to the absolute value inequality is the intersection of the two solutions. You will notice the graph has a distinctive appearance, as only one section of the graph is shaded.
For greater than situations, an OR situation is created. Solve for both, and graph the two solutions on a number line; the solution to the absolute value inequality is the union of the two solutions. Represent and solve equations with absolute value.Solve an absolute value equation using the following steps: Get the absolve value expression by itself.
Set up two equations and solve them separately. • When graphing the solution set on a number line: – If the inequality is > or inequality is ≥ or ≤, use brackets [ ] • The absolute value inequality can be transformed into a compound inequality based you should know how to do the following: – Solve, graph, and write .
Section Absolute Value Inequalities PRACTICE EXAMPLE 4 Solve for x: `2 - 1 10 ` Solution The absolute value of a number is always nonnegative and can never be less than Thus this absolute value inequality has no solution.
The solution set is 5 6 or. The graph of the solution set of an absolute value inequality will either be a segment between two points on the number line, or two rays going in opposite directions from two points on the number line.
The ``forget the minus sign" definition of the absolute value is useless for our purposes. Instead, we will mostly use the geometric definition of the absolute value: The absolute value of a number measures its distance to the origin on the real number line. Since 5 is at 5 units distance from the.
How Do You Graph an Inequality or an Infinite Set on a Number Line? Number lines are really useful in visualizing an inequality or a set. In .