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*Aim: Compound Inequalities Course: Adv. Alg. & Trig. Aim: How do we solve compound inequalities?...*

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Symbolically -

Graph the solution set of (x > 1) (x < 5)

x is a number greater than 1 and x is a number less than 5

Compound Inequality

Symbolically -

Graph the solution set of (x > 2) (x < -1)

x is a number greater than or equal to 2 or x is a number greater than -1

0

1

2

3

4

5

6

7

-7

-6

-5

-4

-3

-2

-1

Aim: Compound Inequalities

9 < 3x + 6 and 3x + 6 < 15

{x |x > 4 x < –1}

Solve each separately

Describe each compound inequality.

{x | –3 < x < 3}

x is greater than or equal to 0 or x is less than or equal to -3

x is greater than or equal to -3 and x is less than 3

x is greater than or equal to 5 or x is less than -3

{x | x < –3 x > 0}

{x | x < –3 x > 5}

0

1

2

3

4

5

6

7

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-7

-6

-5

-4

-3

-2

-1

Model Problem

The ideal length of a both is 13.48 cm. The length can vary from the ideal by at most 0.03 cm. A machinist finds one both that is 13.67 cm long. By how much should the machinist decrease the length so the both can be used?

x = # cm to remove

13.45 < 13.67 – x < 13.51

Symbolically -

Graph the solution set of (x > 1) (x < 5)

x is a number greater than 1 and x is a number less than 5

Compound Inequality

Symbolically -

Graph the solution set of (x > 2) (x < -1)

x is a number greater than or equal to 2 or x is a number greater than -1

0

1

2

3

4

5

6

7

-7

-6

-5

-4

-3

-2

-1

Aim: Compound Inequalities

9 < 3x + 6 and 3x + 6 < 15

{x |x > 4 x < –1}

Solve each separately

Describe each compound inequality.

{x | –3 < x < 3}

x is greater than or equal to 0 or x is less than or equal to -3

x is greater than or equal to -3 and x is less than 3

x is greater than or equal to 5 or x is less than -3

{x | x < –3 x > 0}

{x | x < –3 x > 5}

0

1

2

3

4

5

6

7

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-7

-6

-5

-4

-3

-2

-1

Model Problem

The ideal length of a both is 13.48 cm. The length can vary from the ideal by at most 0.03 cm. A machinist finds one both that is 13.67 cm long. By how much should the machinist decrease the length so the both can be used?

x = # cm to remove

13.45 < 13.67 – x < 13.51