Solving One- and Two-Step Absolute Value Inequalities The same Properties of Inequality apply when solving an absolute value inequality as when solving a regular inequality. If the absolute value of the variable is more than the constant term, then the resulting graph will be two rays heading to infinity in opposite directions.
Review, as needed, how to solve absolute value inequalities. A quick way to identify whether the absolute value inequality will be graphed as a segment between two points or as two rays going in opposite directions is to look at the direction of the inequality sign in relation to the variable.
What are these two values? Instructional Implications Review the concept of absolute value and how it is written.
The correct graph is a segment, beginning at the point 0. Can you describe in words the solution set of the first inequality?
Instructional Implications Provide feedback to the student concerning any errors made in solving the first inequality or representing its solution set. A A ray, beginning at the point 0. What would the graph of this set of numbers look like? Model using simple absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem.
Represents the solution set as a conjunction rather than a disjunction. The main difference is that in an absolute value inequality, you need to evaluate the inequality twice to account for both the positive and negative possibilities for the variable.
Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem? If needed, clarify the difference between a conjunction and a disjunction.
However, the student is unable to correctly write an absolute value inequality to represent the described constraint. The constant is the maximum value, and the graph of this will be a segment between two points.
A ray beginning at the point 0. Can you reread the first sentence of the second problem? The student does not understand how to write and solve absolute value inequalities.
Examples of Student Work at this Level The student: Since the inequality actually had the absolute value of the variable as less than the constant term, the right graph will be a segment between two points, not two rays.
Provide additional examples of absolute value inequalities and ask the student to solve them. Examples of Student Work at this Level The student correctly writes and solves the first inequality: The student correctly writes the second inequality as or.
How can you represent the absolute value of an unknown number? C A ray, beginning at the point 0.Model using absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem. For example, given the statement “all of the employees have salaries, s, that are within $10, of the mean salary, $40,” guide the student to model the range of incomes with an absolute value inequality.
The absolute number of a number a is written as $$\left | a \right |$$ And represents the distance between a and 0 on a number line. An absolute value equation is an equation that contains an absolute value expression.
Solve + Graph + Write Absolute Value Inequalities This lesson is all about putting two of our known ideas, Absolute Value and Inequalities, together in order to Solve Absolute Value Inequalities. Free absolute value inequality calculator - solve absolute value inequalities with all the steps.
Type in any inequality to get the solution, steps and graph. Identifying the graphs of absolute value inequalities. If the absolute value of the variable is less than the constant term, then the resulting graph will be a segment between two points.
If the absolute value of the variable is more than the constant term, then the resulting graph will be two rays heading to infinity in opposite directions. The other case for absolute value inequalities is the "greater than" case.
Let's first return to the number line, and consider the inequality | x | > 2. The solution will be all points that are more than two units away from zero.Download