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Chapter 5

Chapter 5. Solving Linear Inequalities. 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?.

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Chapter 5

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  1. Chapter 5 Solving Linear Inequalities

  2. 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 13,426< 14,587 13,426 +1200 < 14,587+1200 14,626 < 15,287

  3. 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

  4. Graphing Inequalities -5 0 5 • Graph t < 5 • Graph t > 5 • Graph t ≤ 5 • Graph t ≥ 5 -5 0 5 -5 0 5 -5 0 5 If variable is < or > graph using an open circle If variable is ≤ or ≤ graph using a closed circle

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

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

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

  8. 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

  9. Practice • Page 286 12 - 40, every 4th

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