Still for others, it will be to investigate these new problems in the challenging absolute value equations. So in the introduction activity, i have students complete a hands on activity with a table partner. The corner point of the graph, called the occurs at the origin. 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. When solving equations with absolute value we can end up with more than one possible answer. When solving absolute value equations, remember that there can be two solutions, because the absolute value of a number and its opposite are the same. For other students, this might be trying a more challenging level of this assessment. The 2 separate inequalities come from when you split the inequality once the absolute value is isolated. Absolute value which can be written in interval notation as. And at first, this looks really daunting, but the key is to just solve for this absolute value expression and then go from there. Solving simpler absolutevalue equations purplemath. In this case we have a quadratic in the absolute value bars.
So its 4 times the absolute value of x plus 10 plus 4 is equal to 6 times the absolute value of x plus 10 plus 10. 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. Here you will find hundreds of lessons, a community of teachers for support, and materials that are always up to date with the latest standards. Observe that this solution set consists of all x that are within 4 units of 3 on a number line figure e. Below is the general approach on how to break them down into two equations. Solving absolute value equations is as easy as working with regular linear equations. To clear the absolute value bars, i must split the equation into its two possible two cases, one each for if the contents of the absolute value bars that is, if the argument of the absolute value is negative and if its nonnegative that is, if its. Greater than or statements and less than and statements.
Once each student is clear on their expectations, have everyone get started and circulate to make sure that each student is engaged in their task. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. 37 exit quiz absolute value equations and inequalities free. To solve absolute value equations, first isolate the absolute value terms by moving anything outside of the vertical bars to the other side of the equation. Algebra equations absolute value equations easy youtube. We will look at equations with absolute value in them in this section. So its negative 2 times the absolute value of x plus 10 is equal to, well the whole point of this, of the 6 times the absolute value of x plus 10 minus 6 times the absolute value of x plus 10 is to make those cancel out, and then you have 10 minus 4, which is equal to 6. Find all the real valued solutions to the equation.
Intro to absolute value inequalities video khan academy. Yesterday we discussed that the absolute value of a number is the numbers distance from zero on the number line. The absolute value of a number is the number of units it is from 0 on the. They are the same distance from 0 on the number line, but in opposite directions. E x2o051 2s nkzuut 5aw ks0ozf tt0w 4a r8eq 4l ql wc5.
Linear inequalities symbols verify that a given value is a solution to an inequality the solution set of a linear inequality number line interval notation. Algebra 34 unit 1 absolute value functions and equations. In the final two sections of this chapter we want to discuss solving equations and inequalities that contain absolute values. As we prepare for the class to end, i say to students, from time to time, i am going to give you a grade not on your actual work, but on your own reflection on and analysis of your work. On questions 1 thru 14, did the student evaluate the questions correctly.
So if an x meets both of these constraints, its absolute value is definitely going to be less than 12. Absolute value equations worksheets math worksheets. To download worksheet on solving absolute value equations as pdf document, please click here. Solving absolute value equations 2 cool math has free online cool math lessons, cool math games and fun math activities. Dont let the fact that there is a quadratic term in the absolute value throw you off. 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. Literal equations, inequalities, and absolute value. Identify what the isolated absolute value is set equal to a. This problem works exactly the same as the previous problems. For your answer choose the values that make the equation true. Finally, we look at algebraic expressions, equations, and inequalities that involve absolute value.
Free absolute value equation calculator solve absolute value equations with all the steps. Now, we want to solve for the absolute value of x plus 10. Absolute value equations worksheet 1 rtf absolute value equations worksheet 1 pdf view answers. The following properties of the absolute value function need to be memorized. Even though the numbers 5 and 5 are different, they do have something in common. The only additional key step that you need to remember is to separate the original absolute value equation into two parts. An extraneous solution is an apparent solution that must be rejected because it does not satisfy the original equation. The absolute value of negative 11, only 11 away from 0. Solving absolute value inequalities combine the strategies you used in. This study was designed to determine to what extent solving absolute value equations and inequalities by. You know, you take the absolute value of negative 6, thats only 6 away from 0. The absolute value of a number will be 0 only if that number is 0.
Jun 09, 2014 finally, we look at algebraic expressions, equations, and inequalities that involve absolute value. Solve an absolute value equation using the following steps. To solve absolute value equations, remember to do the following. Determine the type of number the absolute value expression is equal to a. Absolute value equations equations with a variable or variables within absolute value bars are known as absolute value equations. Let me just rewrite it so that the absolute value expression really jumps out. Absolute value equations worksheet 2 here is a another 16 problem multiple choice worksheet where you will determine the solutions to equations containing absolute value.
Absolute value equations and inequalities activity. If there is not a unique solution, state whether there is. Test each possible solution by replacing the variable with each possible 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. Isolate the absolute value expression on one side of. Example click to try about absolute value equations. Solving absolute value equations and inequalities on a. To solve reallife problems, such as finding recommended weight ranges for sports equipment in ex.
So something that meets both of these constraints will satisfy the equation. Jay high school santa rosa county florida september 22, 2001 solving absolute value equations checklist 1. To this point weve only worked problems that have linear terms in the absolute value bars. Since the absolute variable can represent 2 numbers, then solve for the negative value by putting a negative. Teaching absolute value equations and inequalities.
Before look at the worksheet, if you would like to know the basic stuff about solving absolute value equations. In order to solve equations or inequalities with absolute value, we need to rewrite them without absolute value, solve them and if necessary check the solutions obtained. This free worksheet contains 10 assignments each with 24 questions with answers. Use absolute value equations and inequalities to solve reallife problems, such as finding acceptable weights in example 4.
Steps for solving absolute value inequalities h 25 everett community college tutoring center there are two types of absolute value inequalities. One of the four possible cases is checked as follows. For any two real numbers x and y, we have jxyj jxjjyj. The purpose of this lesson is for my students to develop a conceptual understanding of what absolute value means, and apply it to solving absolute value equations and inequalities. Included in this set are 24 one step absolute value equation problem task cards, a student answer sheet, and an answer key. Absolute value equations absolute value inequalities. Every absolute value inequality is a compound inequality. All an absolute value inequality does is talk about the distance away from zero so when working with these inequalities you have two. To solve reallife problems such as finding the wavelengths of different colors of fireworks in exs. Next, solve for the positive value of the equation by isolating the variable. We will look at equations with absolute value in them in this section and well look at inequalities in the next section. This is because what is in the absolute value can be either negative or positive and we must account for both possibilities when solving equations. Absolute value equations and inequalities activity free.
Why you should learn it goal 2 goal 1 what you should learn 6. You should check each solution by plugging them into the given equation. Students are given a onestep absolute value equation problem and are asked to solve it. An extraneous solution is an apparent solution that must be rejected. Many students struggle with solving absolute value equations and inequalities because they do not have an understanding of the underlying concepts. Introduction to absolute value equations and inequalities. Absolute value equations and inequalities cool math. Why you should learn it goal 2 goal 1 what you should learn 1.