Greater than or statements and less than and statements. Literal equations, inequalities, and absolute value. All an absolute value inequality does is talk about the distance away from zero so when working with these inequalities you have two. We will look at equations with absolute value in them in this section and well look at inequalities in the next section. Many students struggle with solving absolute value equations and inequalities because they do not have an understanding of the underlying concepts. Students are given a onestep absolute value equation problem and are asked to solve it. Included in this set are 24 one step absolute value equation problem task cards, a student answer sheet, and an answer key. In the final two sections of this chapter we want to discuss solving equations and inequalities that contain absolute values.
Find all the real valued solutions to the equation. And at first, this looks really daunting, but the key is to just solve for this absolute value expression and then go from there. Type in any equation to get the solution, steps and graph this website uses cookies to ensure you get the best experience. An extraneous solution is an apparent solution that must be rejected. The absolute value of negative 11, only 11 away from 0. You should check each solution by plugging them into the given equation. Why you should learn it goal 2 goal 1 what you should learn 1. 37 exit quiz absolute value equations and inequalities free. They are the same distance from 0 on the number line, but in opposite directions. So something that meets both of these constraints will satisfy the equation. So in the introduction activity, i have students complete a hands on activity with a table partner. If there is not a unique solution, state whether there is.
The 2 separate inequalities come from when you split the inequality once the absolute value is isolated. For other students, this might be trying a more challenging level of this assessment. 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. 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.
Even though the numbers 5 and 5 are different, they do have something in common. 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. The absolute value of a number will be 0 only if that number is 0. You know, you take the absolute value of negative 6, thats only 6 away from 0. To solve reallife problems, such as finding recommended weight ranges for sports equipment in ex. For any two real numbers x and y, we have jxyj jxjjyj. In this case we have a quadratic in the absolute value bars. The absolute value of a number is the number of units it is from 0 on the. 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. Intro to absolute value inequalities video khan academy.
Really clear math lessons prealgebra, algebra, precalculus, cool math games, online graphing calculators, geometry. 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. Why you should learn it goal 2 goal 1 what you should learn 6. The most important about the absolute value of an algebraic expression, is that we can simplify them if we know the sign of the expression inside the absolute value symbol. Teaching absolute value equations and inequalities.
On questions 1 thru 14, did the student evaluate the questions correctly. An extraneous solution is an apparent solution that must be rejected because it does not satisfy the original equation. Before look at the worksheet, if you would like to know the basic stuff about solving absolute value equations. Finally, we look at algebraic expressions, equations, and inequalities that involve absolute value.
Dont let the fact that there is a quadratic term in the absolute value throw you off. Solving absolute value equations and inequalities on a. Absolute value equations and inequalities activity. Use absolute value equations and inequalities to solve reallife problems, such as finding acceptable weights in example 4.
Algebra equations absolute value equations easy youtube. 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. So if an x meets both of these constraints, its absolute value is definitely going to be less than 12. Next, solve for the positive value of the equation by isolating the variable. Identify what the isolated absolute value is set equal to a.
Below is the general approach on how to break them down into two equations. Every absolute value inequality is a compound inequality. 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. Solving simpler absolutevalue equations purplemath. Absolute value equations and inequalities activity free.
When solving equations with absolute value we can end up with more than one possible answer. Absolute value equations and inequalities cool math. 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. Since the absolute variable can represent 2 numbers, then solve for the negative value by putting a negative. Isolate the absolute value expression on one side of. To solve reallife problems such as finding the wavelengths of different colors of fireworks in exs. Still for others, it will be to investigate these new problems in the challenging absolute value equations. 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. Steps for solving absolute value inequalities h 25 everett community college tutoring center there are two types of absolute value inequalities. Algebra 34 unit 1 absolute value functions and equations. Solving absolute value inequalities combine the strategies you used in. 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.
E x2o051 2s nkzuut 5aw ks0ozf tt0w 4a r8eq 4l ql wc5. Yesterday we discussed that the absolute value of a number is the numbers distance from zero on the number line. Free absolute value equation calculator solve absolute value equations with all the steps. For your answer choose the values that make the equation true. Jun 09, 2014 finally, we look at algebraic expressions, equations, and inequalities that involve absolute value. To solve absolute value equations, remember to do the following. 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. 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. Solving absolute value equations 2 cool math has free online cool math lessons, cool math games and fun math activities. Let me just rewrite it so that the absolute value expression really jumps out. 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.
Prealgebra solving inequalities lessons with lots of worked examples and practice problems. Absolute value equations worksheets math worksheets. Introduction to absolute value equations and inequalities. This study was designed to determine to what extent solving absolute value equations and inequalities by. Absolute value equations equations with a variable or variables within absolute value bars are known as absolute value equations. Absolute value equations worksheet 1 rtf absolute value equations worksheet 1 pdf view answers. Absolute value equations absolute value inequalities.
To this point weve only worked problems that have linear terms in the absolute value bars. 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. The only additional key step that you need to remember is to separate the original absolute value equation into two parts. Determine the type of number the absolute value expression is equal to a.
Test each possible solution by replacing the variable with each possible value. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. We will look at equations with absolute value in them in this section. 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. This free worksheet contains 10 assignments each with 24 questions with answers. Jay high school santa rosa county florida september 22, 2001 solving absolute value equations checklist 1. Solving absolute value equations is as easy as working with regular linear equations. Now, we want to solve for the absolute value of x plus 10. Observe that this solution set consists of all x that are within 4 units of 3 on a number line figure e. 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. This problem works exactly the same as the previous problems.