### About Interval Notation:

When solving linear inequalities in one variable, the solution is often a range of numbers or an interval. To display an interval, we have a special type of notation, known as interval notation. We can also use set-builder notation or graph the interval using a number line.

Test Objectives

- Demonstrate the ability to write an interval using interval notation
- Demonstrate the ability to write an interval using set-builder notation
- Demonstrate the ability to graph an interval on a number line

#1:

Instructions: Write each in interval notation, set-builder notation, and graph the interval.

a) x ≥ 9

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#2:

Instructions: Write each in interval notation, set-builder notation, and graph the interval.

a) x < -7

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#3:

Instructions: Write each in interval notation, set-builder notation, and graph the interval.

a) x > 2

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#4:

Instructions: Write each in interval notation, set-builder notation, and graph the interval.

a) -9 ≤ x ≤ 9

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#5:

Instructions: Write each in interval notation, set-builder notation, and graph the interval.

a) -4 < x ≤ 2

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Written Solutions:

#1:

Solutions:

a) [9, ∞) - interval notation

{x | x ≥ 9} - set-builder notation

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#2:

Solutions:

a) (-∞, -7) - interval notation

{x | x < -7} - set-builder notation

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#3:

Solutions:

a) (2, ∞) - interval notation

{x | x > 2} - set-builder notation

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#4:

Solutions:

a) [-9, 9] - interval notation

{x | -9 ≤ x ≤ 9} - set-builder notation

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#5:

Solutions:

a) (-4, 2] - interval notation

{x | -4 < x ≤ 2} - set-builder notation