Chapter 6: Solving and Graphing Linear Inequalities



Chapter 6: Solving and Graphing Linear Inequalities

OBJECTIVES: Solve and graph linear inequalities in one variable

STANDARDS: 2.1, 2.2, 2.4, 2.5, 2.8

I. Solving One Step Linear Inequalities

A. Vocabulary

1. Graph –

2. Equivalent Inequalities –

B. Review of Symbols and Graphing

1.

2.

3.

4.

5.

C. Solving & Graphing One Step Inequalities

1.

2.

3.

4.

II. Solving Multi-Step Linear Inequalities

OBJECTIVES: Solve and graph linear inequalities in one variable with multi-steps

STANDARDS: 2.1, 2.2, 2.4, 2.5, 2.8

A. Examples

1.

2.

B. Real Life Situations

1. In 1990 Nashville, Tennessee, had a population of 985,000. From 1990 through 1996, the population increased at an average rate of about 22,000 per year. Write a linear model for the population of Nashville.

2. You start growing geraniums form seed and plan to sell potted plants for Mother’s day. It costs you $1.75 to pot and grow each plant. If you sell each plant for $3.25, how many plants will you need to sell if you want to make a profit of at least $150?

III. Compound Inequalities

OBJECTIVES: Write, solve, and graph compound inequalities

STANDARDS: 2.1, 2.2, 2.4, 2.5, 2.8

A. Vocabulary

1. Compound Inequalities –

B. Writing Compound Inequalities

1. All real numbers that are greater than zero and less than or equal to 4.

2. All real numbers that are less than –3 or greater than 0.

3. Water is a nonliquid when the temperature is 320 F or below, or is at least 2120 F.

C. Solving with AND or OR (SPECIAL inequalities)

1.

2.

3.

4. You live three miles from school and your friend lives two miles from the same school.

a. Find the minimum distance between your home and your friend’s home.

b. Find the maximum distance between your home and your friend’s home.

c. Write an inequality that describes the possible distance between your home and your friend’s home.

IV. Solving Absolute Value Equations and Inequalities

OBJECTIVE: solve absolute value equations and inequalities

STANDARDS: 2.1, 2.2, 2.4, 2.5, 2.8

A. Vocabulary

1. Absolute value – the distance between the origin and real number

must be a positive answer; inside symbol can either be positive or negative

B. Examples of Equations

1. │x – 2 │ = 5

2. │x + 4 │ = 8

3. │2x – 7 │ - 5 = 4

C. Examples of Inequalities

< & < use “and” > & > use “or”

1. │x – 4 │ < 3

2. │x + 9 │ < 1

3. │2x + 1 │ - 3 > 6

4. │3x - 3 │ + 4 > 10

V. Graphing Linear Inequalities in Two Variables

OBJECTIVES: graph linear inequality in two variables; use graphing calculators to check results

STANDARDS: 2.1, 2.2, 2.4, 2.5, 2.8

A. Vocabulary

1. Linear Inequality – an inequality that can be written ax + by < c, ax + by > c, ax + by < c, and ax + by > c.

2. Solution of an Inequality – is an ordered pair (x,y) if the inequality is true when the values of x and y are substituted into the inequality

3. half planes – in the coordinate plane, the region on either side of the boundary line

B. Steps to Graphing

1. Graph the equation

Use dashed line for > and <

Use solid line for > and <

This is the boundary line

2. Test a point in both planes

3. If the point is true ( a solution), shade that half plane

C. Examples

1. x > 1

2. y > -2

3. x + y > 3

VI. Stem-and-leaf plots and Mean, Median, and Mode

OBJECTIVES: make and use a stem-and-leaf plot; find mean, median and mode from a list of data

STANDARDS: 2.1, 2.2, 2.4, 2.5, 2.6, 2.8

A. Vocabulary

1. mean

2. median

3. mode

4. measure of central tendency

5. stem-and-leaf plot

B. Example

45 1 52 42 10 40 50 40 7 46 19 35 3 11 31 6 41 12

VII. Box-and-whisker plot

OBJECTIVE: draw, read and interpret a box-and-whisker plot

STANDARDS: 2.1, 2.2, 2.4, 2.5, 2.6, 2.8

A. Vocabulary

1. box-and-whisker plot

2. lower quartile

3. upper quartile

4. extremes

5. median

B. Example

45 51 55 59 64 70 67 61 56 52 49

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