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# Writing absolute value inequalities from graphs

Here is a listing and brief description of the material that is in this set of notes. Linear Systems with Two Variables — In this section we will solve systems of two equations and two variables. Finding Absolute Value Equations and Inequalities Graphically 20 minutes In the previous lesson, students solved absolute value equations.

They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Students use these operations to solve problems. C A ray, beginning at the point 0. We also define the domain and range of a function.

We start with several greater than inequalities. 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.

In other words, the dog can only be at a distance less than or equal to the length of the leash. The first is similar to one found in my absolute value equations lesson.

If time permits, students can complete another problem. We can do that by dividing both sides by 3, just as we would do in a regular inequality. Likewise, even if I do work some of the problems in here I may work fewer problems in class than are presented here. As we will see we will need to be very careful with the potential solutions we get as the process used in solving these equations can lead to values that are not, in fact, solutions to the equation.

In this section we will solve this type of equation. Integer Exponents — In this section we will start looking at exponents. Absolute Value Inequalities — In this final section of the Solving chapter we will solve inequalities that involve absolute value.

We will also work an example that involved two absolute values. A ray beginning at the point 0. We will also introduce the concepts of inconsistent systems of equations and dependent systems of equations. We will use the method with systems of two equations and systems of three equations. Applications — In this section we will look at a couple of applications of exponential functions and an application of logarithms. Write a single absolute value equation that has the following solutions 18) -4 and 4 19) -3 and 11 Solve the following compound Inequalities and then graph the solutions 26) Answers to Absolute Value / Inequalities review (ID: 1) 1) x y −6−4− −6 −4 −2 2 4 6 2) x y −6−4− −6 −4 −2 2 4 6.

Multi-step Inequalities Compound Inequalities Quadratic Inequalities See all Inequalities There are 45 absolute value inequalities worksheets in this page. Convert each absolute value inequalities into two simple linear inequalities and solve the problems. Grade 6» Introduction Print this page. In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers.

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.

Absolute Value of a Number Worksheets. Absolute Value Worksheet 1 — Here is a fifteen problem worksheet that focuses on finding the absolute value of various numbers. This free worksheet includes both positive and negative integers.  