Simple interest compound interest present value future value. A compound inequality consists of two inequalities joined by the word and or the word or a graph of a compound inequality containing the word and is the intersection of the solution set of the two inequalities what they have in common. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. High school math solutions inequalities calculator, absolute value inequalities part ii. Compound inequalities 1 cool math has free online cool math lessons, cool math games and fun math activities. The purpose of this warm up is for students to be able to recognize the difference and importance between the words and, and or. Compound inequalities when solving a linear inequality, the properties of addition and multiplication still hold, with one exception. In this warm up, i provide the students with two real world examples. Notes solving inequalities just like solving an equation except when you multiply or divide by a negative flip the inequality sign. Solving compound inequalities math worksheets 4 kids. When two simple inequalities are combined into one statement by the words and or or the result is called a compound inequality. Compound inequalities a compound inequality is a sentence with two inequality statements joined either by the word or or by the word and. A compound inequality is a sentence with two inequality statements joined either by the word or or by.
Inequalities 32 solving inequalities by adding or subtracting 33 solving inequalities by multiplying or dividing you can use the concepts in this chapter to plan for a fundraising event. Solve each compound inequality and graph its solution. Greater than or statements and less than and statements. In your own words, write the meaning of each vocabulary term. Determine whether the answer should be a union of sets or or an intersection of sets and. Write an inequality that can be used to find the minimum number of weeks you must. These inequality math stations are perfect to help your students make sense of solving and graphing inequalities. Solving compound inequalities you can graph the solutions of a compound inequality involving and by using the idea of an overlapping region. A 3 uail gl 5 srhi tg whjt rs i mr6e hs mexrcv 0ewdu. Unions when an inequality is combined by the word or the compound inequality is formed. Solve inequalities the same way you would solve an equation.
Notes,whiteboard,whiteboard page,notebook software,notebook, pdf,smart,smart technologies ulc,smart board interactive whiteboard. If the absolute value is greater than or greater than or equal to a positive numbe r, set the argument less than the opposite of the number and greater than the number using an or statement in between the two inequalities. Notes inequalities one variable, linear, and systems one variable inequalities inequality symbols. When an inequality is combined by the word or the compound inequality is formed. Students will apply their equation solving ability to inequalities mathematical practice 7 which require a graph of the solution. Solve linear inequalities involving the distributive property. Steps for solving absolute value inequalities h 25 everett community college tutoring center there are two types of absolute value inequalities. Last post, we learned how to solve rational inequalities. Solve compound inequalities containing the word or and graph their. Graph 2 you can graph the solutions of a compound inequality involving or by using the. A compound inequality contains at least two inequality symbols. A compound inequality is an inequality formed by joining two inequalities with the word and or the word or. Divide by the positive value of the variables coefficient. When two simple inequalities are combined into one statement by the words and or or.
Having a deeper understanding for these two words is going to help students be more successful when solving compound inequalities. The absolute value of any number is always zero or a positive value. Free worksheet with answers, bell work, guided notes, exit quiz, power point, lesson plans and more to help teach absolute value equations and inequalities. The following are some examples of compound inequalities. And indicates that both statements of the compound sentence are true at the same time. Each section except the first section contains three levels of compound inequalities worksheets based on either solving or graphing or both.
Notes inequalities one variable, linear, and systems one. All real numbers that are less than or equal to 3 or greater than 6. To solve a compound inequality, first separate it into two inequalities. Teaching absolute value equations and inequalities. Several inequalities can be combined together to form what are called compound inequalities. The levels are classified based on the number of steps that required solving compound inequalities. When two simple inequalities are combined into one statement by the words and or or the result is called a compound.
Student notes work well as guided instruction with the teacher providing examples of what a compound inequality looks like as an inequality. Definition the inequalities you have seen so far are simple inequalities. If the variable is negative, divide by 1 and reverse the sign. To gain access to our editable content join the algebra 1 teacher community. Since the joining word is and, this indicates that the overlap or intersection is the desired result. If the solution results in a statement that is always true, such as 5 3, then the solution is the set of all real numbers. Multistep inequalities we use the same steps to solve multistep inequalities as we did to solve multistep equations just remember. Applied algebra compound inequalities name solve each compound inequality and graph it on a number line. All an absolute value inequality does is talk about the distance away from zero so when working with these inequalities you have two. These inequalities include rational numbers, but do not include compound inequalities. If it is unclear whether the inequality is a union of sets or an intersection of sets. We can represent the solutions to these equations and inequalities by graphing them on a number line. Please copy down the notes below and answer each of the questions.
Chapter 6 solving linear inequalities 316d if the solution is an untrue statement, such as 4 8, there is no solution. Solve compound inequalities combined by the words and or or. Solving compound inequalities algebra 1, linear inequalitites. If the inequalities are joined by the word and, find the intersection of. These printable worksheets are exclusively designed for high school students. The overlapping region represents numbers that belong in set a and set b. Introducing compound inequalities with a foldable i have never been happy with how ive taught compound inequalities in the past. Linear equations and inequalities lecture notes math 1010 compound inequalities two inequalities joined by the word and or the word or give a compound inequality. Most students will not have experience in solving compound.
First, isolate the e xpression involving the absolute value symbol. Solving inequalities multistep solve the following inequalities and graph the solution on the number line. Solve each inequality, graph the solution, and give interval notation of solution. Students will solve, graph, create, interpret, match, and write inequalities. Examine each equation, and then list the order of the five notes that is represented.
Inequalities explore narrative this lesson is taking a skill that students are proficient with hopefully and pushing it a step further. Compound inequalities the inequalities you have seen so far are simple inequalities. Determine all values that make the denominator zero 4. 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. Therefore, the absolute value of any number is always greater than a negative value. Get all the variables on the left and all the numbers on the right of the sign by adding opposites.
Solving inequalities is the same as solving equations. In this post, we will learn how to solve absolute value. Solve p inequalities one variable, linear, and systems one variable inequalities inequality symbols. Compound inequalities worksheets math worksheets 4 kids. This union is worked out as two separate inequalities and then. Ive never really given my students as reason for why we need to even deal with compound inequalities in the first place. Solve linear inequalities involving more that one operation. Solving inequalities by multiplication and division notes solving inequalities by multiplication or division. Draw a number line, and mark all the solutions and critical values from steps 2 and 3 5. All real numbers that are greater than or equal to 2 and less than 2. Solve, graph and give interval notation to the solution of compound inequalities. When you multiply or divide each side of a linear inequality by a negative number, you must reverse the direction of the inequality symbol.
Solve compound inequalities mathematics libretexts. All real numbers that are greater than 8 and less than or equal to 3. When two inequalities are joined by the word and, the solution set consists of all real numbers that satisfy both inequalities. Oct 07, 2016 introducing compound inequalities with a foldable i have never been happy with how ive taught compound inequalities in the past. When two simple inequalities are combined into one statement by the words and or or, the result is called a compound inequality. Coordinate algebra compound inequalities notes date. Inequalities help you determine how to reach your fundraising goals. Selection file type icon file name description size revision time user. Notes inequalities one variable, linear, and systems. Then solve each inequality, writing the solution as a union of the two solutions.
The graph of the solution set is shown in figure 6. The graph of a compound inequality with an and represents the intersection of the graph of the inequalities. Applying the properties of inequalities to solve inequalities a. Solving compound inequalities andor solve the following compound inequalities and graph the solution on the number line. There are three types of compound inequalities which we will investigate in this lesson. Really clear math lessons prealgebra, algebra, precalculus, cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and. Compound inequalities algebra practice khan academy. Isolate the variable on the left side of the inequality. Compound inequality the result of combining two inequalities. Choose one topic from the chapter to explain with detail. In this diagram, set a represents some integer solutions of x 0. If you multiply or divide by a negative number you must switch the sign.