### About Inequalities & Interval Notation:

When we work with a number line that represents the set of real numbers, we can state that numbers increase as we move right and decrease as we move left. Often, we will show the relationship between two or more numbers using inequality symbols such as: "<", or ">". When working with inequalities where variables are involved, we normally use interval notation. This notation allows us to conveniently show a solution that encompasses a range of values. Additionally, we can also graph an interval on a number line, using the same general strategy used with interval notation.

Test Objectives

- Demonstrate an understanding of Inequality Symbols: "<", "≤", ">", and "≥"
- Demonstrate an understanding of how to write an Inequality using Interval Notation
- Demonstrate an understanding of how to graph an Interval on a Number Line

#1:

Instructions: Replace the ? with "<" or ">".

$$a)\hspace{.2em}{-}2 \hspace{.2em}? \hspace{.2em}{-}1$$

$$b)\hspace{.2em}{-}13 \hspace{.2em}? \hspace{.2em}{-}2$$

$$c)\hspace{.2em}0 \hspace{.2em}? \hspace{.2em}{-}5$$

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#2:

Instructions: Write the following in interval notation.

$$a)\hspace{.2em}x < 5$$

$$b)\hspace{.2em}x ≥ -3$$

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#3:

Instructions: Write the following in interval notation.

$$a)\hspace{.2em}{-}9 ≤ x ≤{-}3$$

$$b)\hspace{.2em}{-}12 < x < 5$$

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#4:

Instructions: Graph the given interval on a number line.

$$a)\hspace{.2em}x ≤ 4$$

$$b)\hspace{.2em}x ≤ -6$$

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#5:

Instructions: Graph the given interval on a number line.

$$a)\hspace{.2em}{-}7 ≤ x < 6$$

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}{-}2 <{-}1$$

$$b)\hspace{.2em}{-}13 <{-}2$$

$$c)\hspace{.2em}0 >{-}5$$

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#2:

Solutions:

$$a)\hspace{.2em}(-\infty, 5)$$

$$b)\hspace{.2em}[-3, \infty)$$

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#3:

Solutions:

$$a)\hspace{.2em}[-9, -3]$$

$$b)\hspace{.2em}(-12, 5)$$

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#4:

Solutions:

$$a)$$

$$b)$$

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#5:

Solutions:

$$a)$$