1 College Algebra K/DC Wednesday, 03 December 2014 OBJECTIVE TSW solve and graph the solutions to linear inequalities, three-part inequalities, quadratic.

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College Algebra K/DCWednesday, 03 December 2014

• OBJECTIVE TSW solve and graph the solutions to linear inequalities, three-part inequalities, quadratic inequalities, and rational inequalities.

• ASSIGNMENT DUE– Sec. 1.6: p. 143 (7-12 all, 15-25 odd, 35-42 all, 44-

52 even) wire basket

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Inequalities1.7Linear Inequalities ▪ Three-Part Inequalities

1-3

Subtract 7.

Divide by –2. Reverse the direction of the inequality symbol when multiplying or dividing by a negative number ! !

Solution set:

Solving a Linear Inequality

interval nota on6, ti

set-builder not i6 t n| a ox x

Havens’ Preference

Use interval notation.

Solve & graph:

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Solving a Linear Inequality

Subtract 8.

Add 4x.

Divide by 6.

Solution set:Write the solution set in interval notation and graph it.

5 4 2x x 45 44 2xx x x

Solve & graph:

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Using Brackets vs. Parentheses

With a strict inequality: Use parentheses.

Ex: x > 4

½ > x

With an inequality that includes equals, use a bracket.

Ex: x ≤ 9

x ≥ –1

“Infinity” and “Negative Infinity” ALWAYS get parentheses!!!

4,

1, 2

, 9 1,

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Interval Notation

Always write the ends in numerical order.

Ex: x < –9 (–∞, –9)

not (–9, –∞)

Ex: 8 ≤ x [8, ∞)

not (∞, 8]

Make sure your brackets look like brackets and not squared-off parentheses!

Make sure your parentheses look like parentheses and not rounded-off brackets!

BOTTOM LINE: Write your answers neatly!

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Solving a Three-Part Inequality

Add 8 to all three parts.

Divide by 6.

Write the solution set in interval notation and graph it.

Solution set:

Solve & graph:

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Assignment: Sec. 1.7: p. 155 (13-33 odd) Due before you go to lunch today (black tray).

Solve each inequality. Write each solution set in interval notation and graph.

3) 2 11 8 6x 25) 2 11 x x

2 5 1 5 317) x x 8 3 29 2 71 ) x x x

4 721) 2 5

3

xx

1 2 1 13

3 5 2 1023) x x x

5 5 2 125) 1x 1027) 1 2 4 6x

11 3 1 1729) x 1

431) 52

x

4333) 4

5

x

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Inequalities1.7Quadratic Inequalities ▪ Rational Inequalities

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Solving a Quadratic Inequality

Solve .

Step 1: Find the values of x that satisfy .

or

or

Step 2: The two numbers divide a number line into three regions.

Use closed dots since the inequality symbol includes equality.

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Solving a Quadratic Inequality

Solve .

Step 3: Choose any value in each of the intervals and find the sign of in each of the intervals. 5 3x x

–4 60

4 4 4: 5 3 9 1x

+

0 0: 5 3 5 30x

6 6 6: 5 3 1 9x

– +

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Solving a Quadratic Inequality

Solve .

–4 60+ – +

Step 4: Since (negative), the solution is the interval that makes negative.

2 2 15 0x x 5 3x x

Solution set: [–3, 5]

23 10 7x x

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Solving Quadratic Inequalities

Solve and graph each of the following:

a)

b)

22 3 0x x

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Solving Rational Inequalities

Solve and graph each of the following:

d)

e)

f)

50

3xx

20

1xx

63

2x

x

Assignment: Sec. 1.7: pp. 155-156 (39-44 all, 69-71 all, 73-77 odd, 78) Due on Wednesday, 10 December 2014 (TEST day).

Solve each inequality. Write each solution in interval notation.2 0) 639 x x 2 7 1040 0) x x

2 42) 34 x x

241 2 9 1) 8x x

2 6 16 844) x x 2 ) 4 6 343 x x

00) 4

71x

x

09) 5

63x

x 2

1)1

17x

x

36

) 73 2x

47 5

15)

x

10 5

377)

2x

1

7 3)2

8x