Virginia department of education 2018 1 mathematics instructional plan algebra ii absolute value equations and inequalities strand. 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. Solving inequalities and absolute value equations and inequalities notes. Absolute value equations, inequalities, special cases, distance, tolerance recall. The graph of the solution set is shown in figure 6. Graph an integer on a number line graph 4 on a number line. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. Algebra absolute value inequalities pauls online math notes. Therefore, the absolute value of any number is always greater than a negative value. Even though the numbers 5 and 5 are different, they do have something in common. Chriss doctor recommended that he limit his fat intake to no more than 60 grams a. When it comes to algebra 1 this is probably one of the toughest lessons. Absolute value 5 combining like terms 6 distributive property i 7 adding expressions 8 subtracting expressions 9 writing expressions 10 evaluating expressions 11 solving equations 12 solving inequalities writing equations 14 writing inequalities 15 solving literal equations 16 points on the coordinate plane 17 graphing using slope and.
The shocking revelation of 112 12 practice form information. The next two problems provide modeling opportunities. Write an inequality for the word problem and then solve the inequality. They are the same distance from 0 on the number line, but in opposite directions. If the absolute value is less than zero, there is no solution. All an absolute value inequality does is talk about the distance away from zero so when working with these inequalities you have two methods depending on whether it is a less than statement or a greater than statement that you use to solve these equations. Which inequality could be used to determine if a salary. Acan help you remember the difference greater than rewrite and solve like an or inequality. Absolute value inequalities recall that absolute value is the distance away from zero. The goal of this homework is for students to reinforce the skills learned in the days lesson. Inequalities absolute value inequalities objective. Solving systems using tables and graphs use the chart below to. The absolute value of a number will always be positive.
Solving absolute value equations and inequalities on a number. Real numbers we can represent the real numbers by the set of points on a line. Solving absolute value equations and inequalities day 1 of 2lesson 8. Determine all values that make the denominator zero 4. Decimal to fraction fraction to decimal distance weight time.
Microsoft word absolute value word problems homework. To solve an absolute value equation, isolate the absolute value on one side of the equal sign, and establish two cases. Identify what the absolute value inequality is set equal to a. To solve this type of absolute value equation, first isolate the expression involving the absolute value symbol. Solving absolute value equations and inequalities day 2 of 2 objective. In this section we want to look at inequalities that contain absolute values. Usingproperty 10, thislastinequalityisequivalentto. Solving absolute value equations graphing absolute value functions solving absolute value inequalities our mission is to provide a free, worldclass education to anyone, anywhere.
The 2 separate inequalities come from when you split the inequality once the absolute value is isolated. Absolute value equations and inequalities guided notes. Solving absolute value inequalities combine the strategies you used in. When an inequality has an absolute value we will have to remove the absolute value in order to graph the solution or give interval notation. Mathematics instructional plan absolute value equations. A summary of solving inequalities containing absolute value in s absolute value. Absolute value inequalities pauls online math notes. Draw a number line, and mark all the solutions and critical values from steps 2. The absolute value of a number can be thought of as the distance a number is from zero. Greater than or statements and less than and statements. Recall that absolute value is the distance away from zero. Yesterday we discussed that the absolute value of a number is the numbers distance from zero on the number line. If the absolute value is less than or equal to zero, there is one solution. To gain access to our editable content join the algebra 1 teacher community.
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 are most easily related to distance. Steps for solving absolute value inequalities h 25 everett community college tutoring center there are two types of absolute value inequalities. This is the content of the following useful theorem, called the triangle inequality. People in this survey were allowed to select more than one type of book. All an absolute value inequality does is talk about the distance away from zero so when working with these inequalities you have two. When solving equations with absolute value we can end up with more than one possible answer. The final question ask student to describe what the graph of an absolute value equation with one.
Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. Student notes work well as guided instruction with the teacher providing examples and specific instruction of how to solve and graph absolute value inequalities. Integers, opposites, absolute value opposites and absolute values. In this final section of the solving chapter we will solve inequalities that involve absolute value. Identify what the isolated absolute value is set equal to a.
Solve, graph and give interval notation for the solution to inequalities with absolute values. Choose one topic from the chapter to explain with detail. We have an algebra 2 lesson that does a good job of explaining this. Learn exactly what happened in this chapter, scene, or section of absolute value and what it means. Jan 27, 2017 would you rather listen to the lesson. Absolute value equations and inequalities guided notes notes. Value 3 of 18 60315 notes, examples and exam questions unit 3. The absolute value of a number is the number of units it is from 0 on the. The absolute value gives us the size or magnitude of a number. Absolute value a45 is always less than or equal to the sum of the absolute values. First, isolate the e xpression involving the absolute value symbol.
Steps for solving linear absolute value inequalities. Absolute value inequalities lone star college system. Absolute value inequalities student notes and practice to complement the introduction to solving absolute value inequalities. The absolute value gives the distance from a value a to zero on a number line. If youre seeing this message, it means were having trouble loading external resources on our website. Properties of absolute value inequalities let k represent a positive real number. Every absolute value inequality is a compound inequality. Greater than rewrite and solve like an or inequality. As we will see the process for solving inequalities with a i. When an inequality has an absolute value we will have to. Solving absolute value equations and inequalities on a. Many students struggle with solving absolute value equations and inequalities because they do not have an understanding of the underlying concepts.
Teaching absolute value equations and inequalities. Less than rewrite and solve like an and inequality. By definition, the equation x 3 can be solved by finding real numbers at a distance of three units from 0. Sal introduces the concept of inequalities that contain absolute value expressions, and solves a bunch of examples. Concept cheat sheet adding integers 1 subtracting integers 2 multiplying integers 3 dividing integers 4 absolute value 5 combining like terms 6 distributive property i 7. In the previous section we solved equations that contained absolute values. Eleventh grade lesson absolute value inequalities betterlesson. These sheets teach the concepts as they are presented in the algebra class software. Absolute value functions and graphs real world applications. This study was designed to determine to what extent solving absolute value equations and inequalities by. There are two types of absolute value inequalities. The absolute value of any number is always zero or a positive value. Intro to absolute value inequalities video khan academy.
Solving absolute value equations and inequalities primary sol. Solving absolute value equations graphing absolute value functions solving absolute value inequalities. 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. Angles and sides, area, laws of sines and cosines notes. Fall2007 now,letsdividebothsidesofthislastinequalityby. The first six problems ask students to solve absolute value inequalities of varying difficulty.
Isolate the absolute value expression on one side of the inequality symbol. Algebra i notes linear inequalities in one variable and unit. Algebra absolute value inequalities practice problems. To solve for x, we must find all values of x that are 5 units away from 0 on the number line. A value becomes absolute if we decide to disregard the opposite negative nature of numbers. Mathematics instructional plan absolute value equations and.
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