## Math 7B, Lesson 7, Spring 2022, 3/27/2022

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Chapter 11.4 Applications of Simple Inequalities.

Problem-solving Strategy

1. Read the question carefully. Identify the unknown quantity.
2. Use a letter, say x, to represent the unknown.
3. Express some other quantities in the question in terms of x.
4. Set up an inequality using the given information.
5. Solve the inequality.
6. Write down the solution of the problem in words.

A lot of examples in class.

HW Assignment

• Handout: two pages
• Workbook: page 20-22, problem #19 – #30.

## 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

## Math 7B, Lesson 5, Spring 2022, 3/13/2022

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## Chapter 11.1 Solving Simple Inequalities1. Idea of inequality

• An inequality is a statement that indicates that one quantity is less than or greater than another. You can write inequalities using symbols such as ” <“, “> “, “<=”, or “>=”.
• 3x < 10
• x < 10/3 All values of x that satisfy the inequality above are called the solutions of the inequality.

## 2. Solving an inequality

• In class, explore the properties of simple inequalities.
• If a > b and k > 0, then ka > kb
• if a < b, and k > 0, then ka < kb
• Lot’s of examples and exencise in class.

## 3. HW:

• Handout: 2 pages
• Workbook: page 17, #1, #2, #3, #4; page 18, #5, #6

## Math 7B, Lesson 4, Spring 2022, 3/6/2022

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Exam: coordinates and linear graphs.

Review materials and exam page are in the Google Classroom.