Part one notes of solving absolute value equations. The only additional key step that you need to remember is to separate the original absolute value equation into two parts. The same thinking is used for absolute value equations. The important thing to remember is that the absolute value means the equation inside the bars may be positive or negative. Absolute value equations and inequalities guided notes. Isolate the absolute value expression on one side of the equation. Absolute value equations when solving absolute value equations, remember you are creating two separate problems to solve. Absolute value equationsalgebrasolving basic equationsmaintaining a balanceequations with multiple stepsabsolute value equationsequations with multiple variablesif youre trying to solve an equation containing a variable thats trapped inside absolute value bars, youll need to.
This includes steps inside and outside the absolute value expression, with examples of no solution as well. Determine the type of number the absolute value expression is equal to a. Mathematics instructional plan absolute value equations. Worksheet given in this section will be much useful for the students who would like to practice problems on solving absolute value equations. Therefore, the absolute value of any number is always greater than a negative value. Solving absolute value equations graphically absolute value equations differ from linear equations in that they may have two solutions.
Eleventh grade lesson absolute value equations betterlesson. Solving absolute value equations notes day 1 free download as word doc. Eighth grade lesson graphing absolute value functions day 1. In this case we have a quadratic in the absolute value bars. Solve an absolute value equation using the following steps. The 2 separate inequalities come from when you split the inequality once the absolute value is isolated. Greater than or statements and less than and statements. So, whether youre teaching absolute value before another topic, or introducing it for the first time, here are 11 absolute value activities that will help student understand and remember absolute value. Graph an integer on a number line graph 4 on a number line. They are guided notes that include examples and opportunities for students to practice problems on their own. We have an algebra 2 lesson that does a good job of explaining this. Solving absolute value inequalities combine the strategies you used in. Solving absolute value equations perhaps you remember from a previous math class the concept of absolute value. They are the same distance from 0 on the number line, but in opposite directions.
Yesterday we discussed that the absolute value of a number is the numbers distance from zero on the number line. The highest or lowest point on the graph of an absolute value function is called the vertex. The absolute value of a number is the number of units it is from 0 on the. We will look at equations with absolute value in them in this section and well look at inequalities in the next section. Notes and examples weve focused our attention this year on working with linear equations. Absolute value equations the equation x 3 is translated as x is 3 units from zero on the number line. As we investigate what happens for an equation with an absolute value part, we find that the graph for these kinds of. From there, we went into story problems involving absolute value equations. For each row in the table, we will graph both examples together. To see why there can be two solutions, you can solve an absolute value equation.
Solution first isolate the absolute value expression on one side of the equation. A summary of solving equations containing absolute value in s absolute value. To download worksheet on solving absolute value equations as pdf document, please click here. Jan 27, 2017 would you rather listen to the lesson. The absolute value of any number is always zero or a positive value. Eighth grade lesson graphing absolute value functions day. To solve an inequality containing absolute value, begin with the same steps as for solving equations with absolute value. Next, i will ask students to create their own absolute value functions and to call out the equations aloud to the group. To solve for x, we must find all values of x that are 5 units away from 0 on the number line. A summary of solving inequalities containing absolute value in s absolute value. Absolute value functions and graphs real world applications. Integers, opposites, absolute value opposites and absolute values. This packet helps students practice how to solve simple absolute value equations.
Every absolute value inequality is a compound inequality. Rewriting equations to solve for specific variables thursday 925 lesson 3. Solving an absolute value equation the absolute value of a number x, written as x, represents the distance from a number x to 0 on the number line. When solving equations with absolute value we can end up with more than one possible answer. Solving inequalities containing absolute value sparknotes. An extraneous solution is a solution that emerges from the process of solving the problem, but is not a.
My lesson absolute value equations presentation includes detailed presenter notes. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. Notes,whiteboard,whiteboard page,notebook software,notebook, pdf,smart,smart technologies ulc,smart board interactive. Now, we want to give you your first taste of something that is not linear. Ixl solve absolute value equations algebra 2 practice. Later, with the whole group, i will use this desmos to show students the effects of a transformation on a function, using absolute value as our example. To this point weve only worked problems that have linear terms in the absolute value bars.
Absolute value equations word problems to begin the class, we started off by working backwards. When faced with an absolute value equation, we need to correctly utilize the definition of absolute value. To really get it, students need to see absolute value a. The absolute value is isolated on the lefthand side of the equation, so its already set up for me to split the equation into two cases. Value 3 of 18 60315 notes, examples and exam questions unit 3. When it comes to algebra 1 this is probably one of the toughest lessons. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. Teaching absolute value equations and inequalities. Here is a set of practice problems to accompany the absolute value equations section of the solving equations and inequalities chapter of the. Vocabulary the absolute value of a number x, writtenx, is the distance, x units away from zero on the number line. Notice, on the number line shown in figure 1, that two different numbers are 3 units away from zero, namely, 3 and 3. Absolute value equations scavenger huntcornell notes and a scavenger hunt activity are inlcuded to introduce and practice solving absolute value equations. Use symmetry to plot a third point and then complete the graph. Each page starts with easier problems that get more difficult as students work through the packet.
Below is the general approach on how to break them down into two equations. Solving inequalities containing absolute value and graphing. Solving absolute value equations is as easy as working with regular linear equations. Absolute value equations and inequalities coursenotes. Page 1 of 2 124 chapter 2 linear equations and functions using absolute value functions in real life interpreting an absolute value function the front of a camping tent can be modeled by the function y. All an absolute value inequality does is talk about the distance away from zero so when working with these inequalities you have two. To clear the absolutevalue bars, i must split the equation into its two possible two cases, one each for if the contents of the absolutevalue bars that is, if the argument of the absolute value is negative and if its nonnegative that is, if its. Absolute value equations and inequalities are most easily related to distance. Before look at the worksheet, if you would like to know the basic stuff about solving absolute value equations, to download solving absolute value. Because the answer to an absolute expression is never negative, we then must realize that each unknown absolute value has the possibility of coming from either a positive or a negative value, producing then two solutions. After doing all 39 problems, students should be more comfortable doing these problems and have a. Improve your math knowledge with free questions in solve absolute value equations and thousands of other math skills. Identify what the isolated absolute value is set equal to a. To solve an absolute value equation, isolate the absolute value on one side of the equal sign, and establish two cases.
I can graph an absolute value function by performing. This lesson is a precursor to the common core algebra 2 standards. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Once students understand how each individual transformation affects an absolute value functions in isolation, we will complete the summary box. The absolute value of a number x, written as x, represents the. An axis of symmetry of the graph of a function is a. First, isolate the e xpression involving the absolute value symbol. Steps for solving absolute value inequalities h 25 everett community college tutoring center there are two types of absolute value inequalities. Solving simpler absolutevalue equations purplemath. Even though the numbers 5 and 5 are different, they do have something in common. By definition, the equation x 3 can be solved by finding real numbers at a distance of three.
When solving equations with absolute value we can end up with. This is indicated with a disjunction, a mathematical statement created by a connecting two other statements with the word or. This problem should provide some great discussion around appropriate models. Absolute value equations and inequalities guided notes notes.
Next, students will use the knowledge that they gained from our whole group discussion to match the equations of absolute value functions with their graphic representation. Algebra absolute value equations pauls online math notes. Learn exactly what happened in this chapter, scene, or section of absolute value and what it means. To solve any absolute value inequalities or equations, it is necessary to have the absolute value section on one side while everything else is on the other side before the equation is split into two equations. In the final two sections of this chapter we want to discuss solving equations and inequalities that contain absolute values.
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