Practice Objectives
- Demonstrate the ability to simplify an expression that contains the absolute value operation
- Demonstrate the ability to solve a simple absolute value equation/inequality
- Demonstrate the ability to find the distance between two points on a number line
Practice Working with the Absolute Value Operation
Instructions:
Answer 7/10 questions correctly to pass.
Problem:
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Finding the Absolute Value of a Number:
- The absolute value operation always gives a non-negative result
- |a| = a, a ≥ 0
- If the number is 0 or positive, keep the number
- Ex: |5| = 5
- |a| = -a, a < 0
- If the number is negative, change the sign from negative to positive
- Ex: |-5| = -(-5) = 5
Distance between Two Points on the Number Line:
- If P and Q are two points on the number line with coordinates a and b, respectively:
- d(P, Q) = |b - a| or d(P, Q) = |a - b|
- The distance between the two points is the absolute value of the difference between their coordinates in either order
Solving a Basic Absolute Value Equation:
- |x| = b, b > 0
- x = b or x = -b
Solving a Basic Absolute Value Inequality:
- |x| < b, b > 0
- -b < x < b
- |x| > b, b > 0
- x < -b or x > b
Step-by-Step:
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