Notes inequalities one variable, linear, and systems one. Linear equations and inequalities lecture notes math 1010 ex. Chapter 10 systems of equations and inequalities notes answers. Wednesday 24 solving and graphing inequalities 2, homework finish all notes 7r 24 notes. This is a powerpoint covering inequalities from number lines, solving and shading regions. Show your steps and write your answer in the space provided. When solving with inequalities, we treat the inequality like an equation except when we multiply or divide by a negative number. Suppose that you have scored at least 3 points in every game this season, and have. Example 9 find the linear inequalities for which the shaded region in the given figure is the solution set. Examine each equation, and then list the order of the five notes that is represented by each. If youd like a pdf document containing the solutions the download tab above contains links to pdfs containing the solutions for the full book, chapter and section. Rewrite the inequality as two separate inequalities. These notes can help introduce and practice graphing linear inequalities.
Draw a number line, and mark all the solutions and critical values from steps 2. This inequality could be solved very easily doing algebra, but it makes a good graphical example. Unions when an inequality is combined by the word or the compound inequality is formed. Remember to label your number line label under the number line examples graph of x graph of x. Data to assess educational inequalities and their causes, we need a measure of educational. The independent practice is made up of both types of compound inequalities.
Inequality a statement that two quantities are not equal solution of an inequality any value that makes the inequality true describing the solutions to inequalities in words. Dont forget to flip the symbol if you multiply or divide by a negative number. A linear equation in one variable is also called a. Solve p inequalities are due to changes in inequalities in the determinants of educational performance the first term on the righthand side of each equation, rather then in their elasticities the second term on the righthand side.
Student application ia assign a worksheet with several onestep inequalities to solve none involving multiplication or division by a negative value. Graphing inequalities guided notes graphing inequalities practice page graphing inequalities frayer models for vocabulary practice2 different warmups 2 per page2 different exit slips 2 per pageworked out answer keys. Notes introduction to inequalities by jennifer hayward tpt. When solving for y, dont forget to flip the inequality symbol if you multiply or divide by a negative. Included are directions for graphing and examples of. Note that the following symbols are used to represent inequalities. Solving inequalities mctyinequalities20091 inequalities are mathematical expressions involving the symbols, guided notes foldable this worksheet can be used to introduce systems of linear inequalities or for students to practice. To solve multistep equations by using inverse operations to isolate the variable, to explain each step in solving the equation, and to check our solutions. Please copy down the notes below and answer each of the questions.
Or if a b, then ac 20 to check the solution, first see whether x 9 makes the equation 3 x 7 20 true. At the top, there is a place for students to make notes about the boundary line solid or dashed depending on the inequality symbol, how to determine which region is supposed to be shaded. Math 1111 lecture notes 1 equations and inequalities 1. Graphing inequalities notes and activities, common core standard. Coordinate algebra compound inequalities notes date. A solution of a linear inequality in two variables is an ordered pair x, y which makes the inequality true. Gcse inequalities notes and worked examples teaching. Powered by create your own unique website with customizable templates. In the problems in this lesson, students are asked to write two solutions to given inequalities. It contains brief notes by way of an explanation, model answers to questions and a question or two for the students to do. Notes,whiteboard,whiteboard page,notebook software,notebook,pdf,smart,smart technologies ulc,smart board interactive whiteboard. We can represent the solutions to these equations and inequalities by graphing them on a number line. If you multiply or divide by a negative number you must switch the sign.
The solution of an inequality is the set of all numbers which satisfy the inequality. Systems of inequalities word problems notes use a system of linear inequalities to solve each problem. Allow us to order sides or angles of triangles by lengths do not give us exact lengths. Inequalities and triangles notes definition of inequality.
After the guided practice, i assign students to work on the independent practice. Math 1111 lecture notes 1 equations and inequalities. We want to follow the same pattern as we did for solving multistep equations. More than 15,000 fans, f, attended the football game last night. Determine all values that make the denominator zero 4. Note that the common solution of 1 and 2 is null set. To graph the solution to an inequality with one variable. Steps for solving absolute value inequalities everett community. Algebra solving equations and inequalities practice. If a, b, and c are real numbers and c is negative, and a bc.
Graphing linear inequalities interactive notes by math dyal tpt. Solving inequalities mctyinequalities20091 inequalities are mathematical expressions involving the symbols, sep 28, 2014 systems of linear inequalities guided notes foldable this worksheet can be used to introduce systems of linear inequalities or for students to practice. Notes inequalities one variable, linear, and systems. Let suppose to have a onevariable or a twovariable inequality given by. It provides the students with more practice to distinguish between and, and or. Solving inequalities is the same as solving equations. Systems of equations and inequalities 101 systems of equations system of linear equations. Students will represent inequalities graphically on a number line, translate an inequality in words to an inequality using symbols and graph, state whether a number is in the solution set of an inequality and write and graph inequalities that represent reallife situations.
I walk around the room while students are working to monitor progress and to assist students one on one or in. Here are a set of practice problems for the solving equations and inequalities chapter of the algebra notes. These are formatted for interactive notebooks and even include areas to doodle. The mathematics of solving linear inequalities is so similar to that of linear equations that most students will have little trouble with the calculations.
When you divide or multiply by a negative number you flip the sign. Even though 9 isnt a solution, its a critical number or. Draw a number line, and mark all the solutions and critical values from steps 2 and 3 5. Throughout the warm up, guided notes, practice, and lesson, students should gain a conceptual understanding of why these different methods for solving a system of equations work. Inequalities sometimes a problem may require us to nd all numbers which satisfy an inequality. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Graphing the solution to an inequality and a system of inequalities. Thinking graphically can help us understand the algebraic procedure for solving nonlinear inequalities. Analyze, solve, and graph linear inequalities instructor notes the mathematics of linear inequalities this unit introduces inequalities. If youd like a pdf document containing the solutions the download tab above contains links to pdf s containing the solutions for the full book, chapter and section. I ask the following questions throughout the lesson. Jan 18, 2016 this is a powerpoint covering inequalities from number lines, solving and shading regions. Algebra solving equations and inequalities practice problems. While students are working the independent practice, they are allowed to talk with their assigned elbow partner for math questions, but they must stay on task.
These are notes used to introduce students to inequalities. Graph all the inequalities on the same coordinate plane. Chapter 10 systems of equations and inequalities notes. The graph of an inequality with one variable is the set of points that represent all solutions of the inequality. Solving inequalities by multiplication and division notes solving inequalities by multiplication or division. Additional copies of the classwork can be printed or copied onto a sheet of labeled notebook paper math 6 classwork.
Chapt 5 notes 20112012 woodland hills school district. The most common inequality symbols are, and to solve an inequality sentence, use exactly the same procedure that you would if it were an equation, with the following exception. An inequality is written like an equation, except the equals sign is replaced by one of the symbols. Example 2 write inequalities from a graph write an inequality that represents the graph.
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