### About Absolute Value & the Distance Between Two Points on a Number Line:

When we think about absolute value, we are thinking about the distance between a number and zero on the number line. Since a distance is always non-negative, meaning it is either zero or some positive value, the absolute value of a number is always non-negative. The absolute value of a number is just the number if it is a non-negative number or the opposite of the number if it's a negative number.

Test Objectives
• Demonstrate an understanding of how to Simplify an Absolute Value Expression
• Demonstrate an understanding of how to Solve a Simple Absolute Value Inequality
• Demonstrate an understanding of how to find the Distance Between Two Points on a Number Line
Absolute Value & the Distance Between Two Points on the Number Line Practice Test:

#1:

Instructions: Simplify each.

$$a)\hspace{.2em}{-}|{-}3|$$

$$b)\hspace{.2em}|{-}5 \cdot 7 + 2^2|$$

#2:

Instructions: Solve each inequality for x.

$$a)\hspace{.2em}|x| > -12$$

$$b)\hspace{.2em}|x| < -8$$

#3:

Instructions: Solve each inequality for x.

$$a)\hspace{.2em}|x| < 7$$

$$b)\hspace{.2em}|x| > 9$$

#4:

Instructions: Find the distance between Point "Q" and Point "R" on the number line.

$$a)\hspace{.2em}Q=-5, R=7$$

$$b)\hspace{.2em}Q=-1, R=8$$

#5:

Instructions: Find the distance between Point "Q" and Point "R" on the number line..

$$a)\hspace{.2em}Q=-3, R=-1$$

$$b)\hspace{.2em}Q=12, R=-15$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}{-}3$$

$$b)\hspace{.2em}31$$

#2:

Solutions:

$$a)\hspace{.2em}\text{All Real Numbers}$$ $$(-\infty, \infty)$$

$$b)\hspace{.2em}\text{No Solution}$$ $$∅$$

#3:

Solutions:

$$a)\hspace{.2em}{-}7 < x < 7$$ $$(-7, 7)$$

$$b)\hspace{.2em}x < -9 \hspace{.25em}\text{or}\hspace{.25em}x > 9$$ $$(-\infty, -9) ∪ (9, \infty)$$

#4:

Solutions:

$$a)\hspace{.2em}12$$

$$b)\hspace{.2em}9$$

#5:

Solutions:

$$a)\hspace{.2em}2$$

$$b)\hspace{.2em}27$$