## Math 7B, Lesson 6, Spring 2022, 3/20/2022

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Chapter 11.2 More Properties of Inequalities & Chapter 11.3 Simple Linear Inequalities

1. For any two numbers, and b, one and only one of the following relationships holds:

• a < b
• a = b
• a > b

2. If a < b and b < c, then a < c

3.  When a number is added to or subtracted from both sides of an inequality, the inequality holds.

• If a < b, then a + k < b + k

4. When both sides of an inequality are multiplied by a non-zero number k, the inequality holds for k > 0, but the inequality sign is reversed for k < 0.

• if a < b and k >0, then ka < kb
• if a < b and k < 0, then ka > kb

5. We can apply the properties of inequalities learned in the previous sections to solve simple linear inequalities in one variable, such as

• 3x + 5 < 17
• 4x -9 > 7x + 8
• represents the solution on a number line

6. HW assignment

• handout: 1 page
• workbook: page 18:#7, #8, #9; page 19: #14, #15, #16, #17, #18

1. For any two numbers, and b, one and only one of the following relationships holds:

• a < b
• a = b
• a > b

2. If a < b and b < c, then a < c

3.  When a number is added to or subtracted from both sides of an inequality, the inequality holds.

• If a < b, then a + k < b + k

4. When both sides of an inequality are multiplied by a non-zero number k, the inequality holds for k > 0, but the inequality sign is reversed for k < 0.

• if a < b and k >0, then ka < kb
• if a < b and k < 0, then ka > kb

5. We can apply the properties of inequalities learned in the previous sections to solve simple linear inequalities in one variable, such as

• 3x + 5 < 17
• 4x -9 > 7x + 8
• represents the solution on a number line

6. HW assignment

• handout: 1 page
• workbook: page 18:#7, #8, #9; page 19: #14, #15, #16, #17, #18