Example 9 find the linear inequalities for which the shaded region in the given figure is the solution set. Dont forget to flip the symbol if you multiply or divide by a negative number. Determine all values that make the denominator zero 4. 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. It provides the students with more practice to distinguish between and, and or. 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. I ask the following questions throughout the lesson. A linear equation in one variable is also called a.
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. 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. Linear equations and inequalities lecture notes math 1010 ex. Systems of inequalities word problems notes use a system of linear inequalities to solve each problem. Example 2 write inequalities from a graph write an inequality that represents the graph. Graph all the inequalities on the same coordinate plane.
In the problems in this lesson, students are asked to write two solutions to given inequalities. 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. Algebra solving equations and inequalities practice problems. These notes can help introduce and practice graphing linear inequalities. Notes introduction to inequalities by jennifer hayward tpt.
When solving with inequalities, we treat the inequality like an equation except when we multiply or divide by a negative number. If you multiply or divide by a negative number you must switch the sign. Included are directions for graphing and examples of. Math 1111 lecture notes 1 equations and inequalities. Math 1111 lecture notes 1 equations and inequalities 1. When you divide or multiply by a negative number you flip the sign. 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. Inequalities and triangles notes definition of inequality. Chapter 10 systems of equations and inequalities notes answers. 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.
Here are a set of practice problems for the solving equations and inequalities chapter of the algebra notes. 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. Please copy down the notes below and answer each of the questions. Notes,whiteboard,whiteboard page,notebook software,notebook,pdf,smart,smart technologies ulc,smart board interactive whiteboard. We want to follow the same pattern as we did for solving multistep equations. Data to assess educational inequalities and their causes, we need a measure of educational. 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.
Even though 9 isnt a solution, its a critical number or. Analyze, solve, and graph linear inequalities instructor notes the mathematics of linear inequalities this unit introduces inequalities. Algebra solving equations and inequalities practice. Gcse inequalities notes and worked examples teaching. Allow us to order sides or angles of triangles by lengths do not give us exact lengths. Student application ia assign a worksheet with several onestep inequalities to solve none involving multiplication or division by a negative value. Thinking graphically can help us understand the algebraic procedure for solving nonlinear inequalities. Let suppose to have a onevariable or a twovariable inequality given by. I walk around the room while students are working to monitor progress and to assist students one on one or in. To graph the solution to an inequality with one variable. Chapt 5 notes 20112012 woodland hills school district. Notes inequalities one variable, linear, and systems one. We can represent the solutions to these equations and inequalities by graphing them on a number line. Chapter 10 systems of equations and inequalities notes.
Remember to label your number line label under the number line examples graph of x graph of x. The independent practice is made up of both types of compound inequalities. Wednesday 24 solving and graphing inequalities 2, homework finish all notes 7r 24 notes. Show your steps and write your answer in the space provided. Graphing linear inequalities interactive notes by math dyal tpt. This is a powerpoint covering inequalities from number lines, solving and shading regions. The graph of an inequality with one variable is the set of points that represent all solutions of the inequality. It contains brief notes by way of an explanation, model answers to questions and a question or two for the students to do.
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. When solving for y, dont forget to flip the inequality symbol if you multiply or divide by a negative. Inequalities sometimes a problem may require us to nd all numbers which satisfy an inequality. Systems of equations and inequalities 101 systems of equations system of linear equations. Notes inequalities one variable, linear, and systems. 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.
Examine each equation, and then list the order of the five notes that is represented by each. A solution of a linear inequality in two variables is an ordered pair x, y which makes the inequality true. Note that the following symbols are used to represent inequalities. Graphing inequalities notes and activities, common core standard. Draw a number line, and mark all the solutions and critical values from steps 2 and 3 5. Coordinate algebra compound inequalities notes date. Jan 18, 2016 this is a powerpoint covering inequalities from number lines, solving and shading regions. 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 formatted for interactive notebooks and even include areas to doodle. Graphing the solution to an inequality and a system of inequalities. Suppose that you have scored at least 3 points in every game this season, and have a season high score of at most 15 points in one game. Draw a number line, and mark all the solutions and critical values from steps 2.
More than 15,000 fans, f, attended the football game last night. Note that the common solution of 1 and 2 is null set. Suppose that you have scored at least 3 points in every game this season, and have. Solving inequalities by multiplication and division notes solving inequalities by multiplication or division. The solution of an inequality is the set of all numbers which satisfy the inequality. 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. Tell whether the ordered pair is a solution of the inequality. If a, b, and c are real numbers and c is negative, and a bc. These are notes used to introduce students to inequalities. Solving inequalities is the same as solving equations. Additional copies of the classwork can be printed or copied onto a sheet of labeled notebook paper math 6 classwork. Or if a b, then ac 20 to check the solution, first see whether x 9 makes the equation 3 x 7 20 true. An inequality is written like an equation, except the equals sign is replaced by one of the symbols. An introduction to solving and graphing inequalities brief overview.
Powered by create your own unique website with customizable templates. The mathematics of solving linear inequalities is so similar to that of linear equations that most students will have little trouble with the calculations. Rewrite the inequality as two separate inequalities. Steps for solving absolute value inequalities everett community. After the guided practice, i assign students to work on the independent practice. 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.
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