objective: section 1.6 solving linear inequalities 1 5 minute check solve the following equations....

Objective: Section 1.6 Solving Linear Inequalities

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5 Minute Check Solve the following equations.

1. 7x – 4 = 5x + 2

2. 10 – 3y = 16y – 9

3. mm5

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2

1

4

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5

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1. How to solve simple inequalities (and graph them on a number line).

2. You will also learn how to solve compound inequalities.

Investigation:1. Write two true inequalities involving integers using <, and one using >. Example -6 < 32. Add, subtract, multiply and divide each side of your inequality by 2 and -2. In each case, decide whether the new inequality is true or false.3. What can you conclude?

What will you learn today?


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Linear Inequalities

Inequalities such as x < 1 and 2n – 3 > 9 are examples of linear inequalities in a single variable.

A solution of an inequality in one variable is a value of the variable that makes the inequality true.

What are some of the solutions to x < 9?


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Graphing InequalitiesThe graph of an inequality in one variable consists of all points on a real number line that correspond to solutions of the inequality.

Graph x > 3.

When do you use an open dot or a closed dot?

How would you graph

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

5n


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1. Solving an Inequality with a Variable on One Side

Example: Solve 5y – 8 < 12

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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You Try Solve 11y – 9 > 13

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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2. Solving an Inequality with Variables on Both Sides

Solve 2x + 1 < 6x – 1

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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You Try Solve 7x + 9 > 10x – 12

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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A Real-World Example The weight w (in pounds) of an Icelandic

saithe is given byW = 10.4t – 2.2

Where t is the age of the fish in years. Describe the ages of a group of Icelandic saithe that weight up to 29 pounds.

292.24.10 t


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Solving Compound Inequalities

A compound inequality is two simple inequalities joined by “and” or “or”. Example:

-2 < x < 1 x < 1 or x > 2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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Solving an “And” Compound Inequality Solve: 10832 t

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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You Try Solve -12 < 3x – 3 < 15

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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You Try Solve -2x + 7 < 3 or 3x + 5 < 2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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4. Solving an “Or” Compound Inequality

Solve: 2x + 3 < 5 or 4x – 7 > 9

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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Homework

Page 45, 13-18 all, 20, 28, 30, 38, 44, 50

objective: section 1.6 solving linear inequalities 1 5 minute check solve the following equations....

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