The inequalities in example 1 are strict inequalities. These printable worksheets are exclusively designed for high school students. Student notes work well as guided instruction with the teacher providing examples of what a compound inequality looks like as an inequality. Isolate a positive x on the left side using algebra reverse the inequality sign when multdivide by a negative less than. Vocabulary inequality solution of an inequality 31 graphing and writing inequalities the athletes on a lightweight crew team must weigh 165 pounds or less. In the case where the compound inequality contains the word or, we combine all the elements of both sets to create one set containing all the elements of each. In this problem, well move the variables to the left side. Compound inequalities word problems flashcards quizlet. The following are some examples of linear inequalities, all of which are solved in this section. Find three consecutive even integers whose sum is between 80 and 91. If it is unclear whether the inequality is a union of sets or an intersection of sets. This type of compound inequality is called a conjunction.
Each high school pdf worksheet contains 10 multiple choices only eight in multi step based on identifying correct solutions for the compound inequalities. As mentioned in the previous step, you would begin by subtracting 7 from both sides. Find three consecutive even integers whose sum is between 46 and 62. A compound inequality is made up of two inequalities connected by the word and or the word or. Get all the variables on the left and all the numbers on the right of the sign by adding opposites. Solving compound inequalities andor solve the following compound inequalities and graph the solution on the number line.
Solve compound inequalities in the form of and and express the solution graphically. Since a compound inequality is really two inequalities in one statement, we must perform the same operations on all three parts of the inequality. The two inequalities would be joined by the word and or or. A compound inequality is simply the combination of two or more inequalities. A compound inequality is just more than one inequality that we want to solve at the same time. Compound inequalities in mathematics, it can be useful to limit the solution or even have multiple solutions for an inequality. For example, the second layer of the earths atmosphere is the stratosphere, which is at least 9 miles and at the most 31 miles over the earths surface. A compound inequality is a statement in which two inequalities are connected by the word and or the word or. It shows you how to graph the solution on a number line and how to.
A compound inequality is a sentence with two inequality statements joined either by the word or or by the word and. For this we use compound inequalities which are inequalities with multiple inequality signs. This union is worked out as two separate inequalities and. Lets take a closer look at a compound inequality that uses or to combine two inequalities. Determine whether the answer should be a union of sets or or an intersection of sets and. When the word that connects both inequalities is and, the solution is. For example, the following are compound inequalities. A compound inequality contains at least two inequality symbols. For example, x 6 or x examples that orgainze compound inequalities by and or or. In the next section you will see examples of how to solve compound inequalities containing and. Compound inequalities worksheets math worksheets 4 kids. There are three types of compound inequalities which we will investi. The following are some examples of compound inequalities. Solving inequalities mctyinequalities20091 inequalities are mathematical expressions involving the symbols, compound inequality includes two inequalities in one statement.
Symbols and vocabulary algebra rules general rules. How to solve inequalities with fractions sciencing. Write an inequality expressing the possible length of the garden plot. Isolate a positive x on the left side using algebra reverse the inequality sign when multdivide by a negative.
A number is a solution to the compound inequality if. The ability to analyze and create linear equations, inequalities, and functions is essential for success in college and career, as is the ability. We know that the total perimeter needs to be less than or equal to 75, because thats all the fencing farmer ted has. The solution of a compound inequality that consists of two inequalities joined with the word and is the intersection of the solutions of each inequality. So 3 compound inequalities using this printable worksheet and interactive quiz. There are three types of compound inequalities which we will investigate in this lesson. Write an inequality where x is the amount of minutes you should bake the cake. Compound inequalities algebra practice khan academy. This compound inequalities foldable covers solving and and or compound inequalities, and writing compound inequalities from a graph. If x is stratosphere, you can write down this compound inequality as. Definition the inequalities you have seen so far are simple inequalities. A of an inequality in one variable is a value of the variable.
Divide by the positive value of the variables coefficient. Solve each compound inequality and graph its solution. Improve your math knowledge with free questions in solve compound inequalities and thousands of other math skills. The acceptable weights for these athletes can be described using an inequality. The first example is about how much a restaurant charges based on age, and the second example is about the two different readings of blood pressure. Before we look at the examples lets go over some of the rules and key words for solving word problems in algebra or any math class. A recipe calls to bake a cake for 20 to 25 minutes. A linear inequality linear expressions related with the symbols. All four examples also ask students to graph the compound ine. Lets do some compound inequality problems, and these are just inequality problems that have more than one set of constraints. Youre going to see what im talking about in a second. Compound inequality using the word and is true if and only if both inequalities are true.
Compound inequalities compound inequalitiestwo inequalities joined by the word and or the word or. A compound inequality includes two inequalities in one statement. The levels are classified based on the number of steps that required solving compound inequalities. Compound inequalities contain two distinct inequalities. A number is a solution to the compound inequality if the number is a solution to both inequalities. Find three consecutive odd integers whose sum is between 75 and 91. Review of basic inequalities essential understanding. In this warm up, i provide the students with two real world examples. Remember, as in the last step on the right, to switch the inequality when multiplying by a negative. Unions when an inequality is combined by the word or the compound inequality is formed. When two simple inequalities are combined into one statement by the words and or or, the result is called a compound inequality. Write the word or phrase that best completes each statement or answers the question. These compound inequalities two or more inequalities in one statement joined by the word and or by the word or. A compound inequality contains at least two inequalities that are separated by either and or or.
In this case, we are looking for a solution to either one of the. Solving and graphing conjunction compound inequalities. Looks like an l for ess than compound inequalities worksheets based on either solving or graphing or both. Multiplying both sides of an inequality by the same number always produces an equivalent inequality. Compound inequalities examples algebra video khan academy. Hopefully by now you better understand the difference in the two types of compound inequalities and you have an idea of what the graph will look like for each type of compound inequality.
Mar 01, 2017 the difference between andor compound inequalities duration. Examples, worksheets, solutions, and activities to help algebra 1 students learn how to solve compound inequalities. Explain the difference between a simple linear inequality and a compound linear inequality. A 3 uail gl 5 srhi tg whjt rs i mr6e hs mexrcv 0ewdu. Compound inequalities 1 cool math has free online cool math lessons, cool math games and fun math activities. This foldable is perfect for a standalone lesson, revie. To solve a compound inequality, first separate it into two inequalities. Determine all values that make the denominator zero 4. Compound inequalities a compound inequality is a sentence with two inequality statements joined either by the word or or by the word and. Sometimes we encounter compound inequalities where the separate solution sets overlap. Feb 16, 2017 this algebra 2 video tutorial focuses on solving compound inequalities with fractions.
In order to better understand these types of inequalities, you will want to study the following lessons. Compound inequalities are two inequalities considered together. Al students earning above a 90 or below a 65 were asked to report to room a for addtiona instructions. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. A number x is greater than j8 and less than or equal to 4. Compound inequalities compound inequalities two inequalities joined by the word and or the word or. Finding domain and range on a graph compound inequalities. Rather than splitting a compound inequality in the form of a inequalities x a, you can more quickly solve the inequality by applying the properties of inequality to all three segments of the compound inequality. The graph of a compound inequality with an and represents the intersection of the graph of the inequalities. Compound inequalities worksheets each section except the first section contains three levels of compound inequalities worksheets based on either solving or graphing or both. Draw a number line, and mark all the solutions and critical values from steps 2 and 3 5.
Its really up to you and whatever way makes more sense. Think about others ways you might use inequalities in real world problems. And indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements. The words and and or are used to describe how the two parts are related. Solve, graph and give interval notation to the solution of compound inequalities. Solve compound inequalities mathematics libretexts. Here you can choose which side of the inequality to get the variables on. Ive tried to provide you with examples that could pertain to your life and come in handy one day. A compound inequality consists of two inequalities that are joined together by the word and or the word or. If the variable is negative, divide by 1 and reverse the sign. Solve each inequality, graph the solution, and give interval notation of solution. Topics include basic singlevariable inequalities, as well as, onestep, twostep, and compound inequalities. For example, the solution set of the compound inequality x 5 and x u 3 contains all values of x that make the inequality x 5 a true.
Chapter 16 heart of algebra heart of algebra questions on the sat math test focus on the mastery of linear equations, systems of linear equations, and linear functions. Really clear math lessons prealgebra, algebra, precalculus, cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. Write an inequality for a persons percentage, x, if he or she has a c in the class. Compound inequality the result of combining two inequalities. Solving compound inequalities algebra 1, linear inequalitites. A compound inequality is an inequality that is formed by the union, or, or the intersection, and, of two simple inequalities. Each high school pdf worksheet contains 10 multiple choices only eight in multistep based on identifying correct solutions for the compound inequalities. River consumes between 510 and 540 calories per day. Compound inequalities is a method to find the variable value for the given compound inequalities. Ixl solve compound inequalities algebra 1 practice. We can either use the word and or or to indicate if we are looking at the solution to both. Several inequalities can be combined together to form what are called compound inequalities.
The pages below all have printable algebra worksheets for teaching students to solve and graph inequalities. Rea world application for compound inequalities and statements the doctor told the mother that the expected weight for the baby for her age was between 20 and 25 pounds. Solve compound inequalities with and now that we know how to solve linear inequalities, the next step is to look at compound inequalities. Solving compound inequalities with fractions using interval. The expected weight must be greater or equal to 20 pounds and less than or equal to 25 pounds. The inequalities you have seen so far are simple inequalities. A compound inequality containing the word and is true only if both inequalities are true. Solving compound inequalities examples, videos, worksheets. An emphasis on graphing the solution set and writing the solution set in setbuilder notation is included. So the first problem i have is negative 5 is less than or equal to x minus 4, which is also less than or equal to. Compound inequalities worksheet solve each inequality and graph its solution.444 898 260 859 711 1594 60 133 673 1384 215 1531 1270 1276 1162 955 945 262 575 678 234 306 821 1256 751 816 81 1267 705 1271 263 901 470