Solving Linear Inequalities Chapter Solving Inequalities by Addition and Subtraction CLE ; SPI Solve problems involving linear equations and linear inequalities.; Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. 5.2 Solving Inequalities by Multiplication and Division CFU ; CLE ; SPI Solve multi-step linear inequalities with one variable and graph the solution on a number line.; Solve problems involving linear equations and linear inequalities.; Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. 5.3 Solving Multi-Step Inequalities CFU ; CLE ; SPI ; SPI Solve multi-step linear inequalities with one variable and graph the solution on a number line.; Solve problems involving linear equations and linear inequalities.; Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value.; Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. 5.4 Solving Compound Inequalities SPI Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. 5.5 Inequalities Involving Absolute Value CFU ; SPI Solve absolute value equations and inequalities (including compound inequalities) with one variable and graph their solutions on a number line.; Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. 5.6 Graphing Inequalities in Two Variables CFU ; CLE ; SPI Graph linear inequalities on the coordinate plane and identify regions of the graph containing ordered pairs in the solution.; Solve problems involving linear equations and linear inequalities.; Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value.

Are the number of students playing volleyball more or less than the number in track and field? How would you write this as a mathematical sentence? Suppose 1200 schools added both sports would this change the situation? Can we show this mathematically? Volleyball < Track & Field 13, < 14, ,426< 14,587 14,626 < 15,287

Addition Property of Inequalities If any number is added to each side of a true inequality, the resulting inequality is also true. If a > b then a + c > b + c Subtraction Property of Inequalities If a > b then a - c > b - c

Inequalities ≤ At most No more than Less than or equal to ≥ At Least No less than Greater than or equal to < Less than Fewer than > Greater than More than

Graphing Inequalities Graph t < 5 Graph t > 5 Graph t ≤ 5 Graph t ≥ 5 If variable is graph using an open circle If variable is ≤ or ≤ graph using a closed circle

Solving Inequalities Solve S – 12 > 65, then Graph on a number line 1.Determine what answer will look like 2.Eliminate Grouping Symbols 3.Eliminate Fractions 4.Add or subtract to isolate variable 5.Divide by Coefficient 6.Check solution S – 12 > S > 77 77

Solving Inequalities Solve 12 ≥ y - 9, then graph on a number line 1.Determine what answer will look like 2.Eliminate Grouping Symbols 3.Eliminate Fractions 4.Add or subtract to isolate variable 5.Divide by Coefficient 6.Check solution 12 ≥ y ≥ y 21

Solving Inequalities Solve 5p + 7 > 6p, then graph on a number line 1.Determine what answer will look like 2.Eliminate Grouping Symbols 3.Eliminate Fractions 4.Add or subtract to isolate variable 5.Divide by Coefficient 6.Check solution 5p + 7 > 6p -5p 7 > p p < 7 7

Write an inequality Four times a number is no more than three times that number plus eight. 4x  3x + 8 Seven times a number is greater than six times that number minus 2. 7x > 6x -2 A number decreased by 8 is at most 14. X – 8  14 A number plus 7 is greater than 2 X + 7 > 2

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