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
#1:
Instructions: Simplify each.
$$a)\hspace{.2em}{-}|{-}3|$$
$$b)\hspace{.2em}|{-}5 \cdot 7 + 2^2|$$
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#2:
Instructions: Solve each inequality for x.
$$a)\hspace{.2em}|x| > -12$$
$$b)\hspace{.2em}|x| < -8$$
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#3:
Instructions: Solve each inequality for x.
$$a)\hspace{.2em}|x| < 7$$
$$b)\hspace{.2em}|x| > 9$$
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#4:
Instructions: Find the distance between Point "Q" and Point "R" on the number line.
$$a)\hspace{.2em}Q=-5, R=7$$
$$b)\hspace{.2em}Q=-1, R=8$$
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#5:
Instructions: Find the distance between Point "Q" and Point "R" on the number line..
$$a)\hspace{.2em}Q=-3, R=-1$$
$$b)\hspace{.2em}Q=12, R=-15$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}{-}3$$
$$b)\hspace{.2em}31$$
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#2:
Solutions:
$$a)\hspace{.2em}\text{All Real Numbers}$$ $$(-\infty, \infty)$$
$$b)\hspace{.2em}\text{No Solution}$$ $$∅$$
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#3:
Solutions:
$$a)\hspace{.2em}{-}7 < x < 7$$ $$(-7, 7)$$
$$b)\hspace{.2em}x < -9 \hspace{.25em}\text{or}\hspace{.25em}x > 9$$ $$(-\infty, -9) ∪ (9, \infty)$$
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#4:
Solutions:
$$a)\hspace{.2em}12$$
$$b)\hspace{.2em}9$$
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#5:
Solutions:
$$a)\hspace{.2em}2$$
$$b)\hspace{.2em}27$$
