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Questions and Answers
What is the approximate average percentage of the Earth's surface area covered by land?
What is the approximate average percentage of the Earth's surface area covered by land?
Which of these has a lower density: the oceanic crust, or the continental crust?
Which of these has a lower density: the oceanic crust, or the continental crust?
What is the correct order of layers, from the Earth's surface to the center?
What is the correct order of layers, from the Earth's surface to the center?
Which part of the Earth's interior is primarily liquid?
Which part of the Earth's interior is primarily liquid?
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Where does most earthquake activity occur?
Where does most earthquake activity occur?
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Flashcards
Image Analysis
Image Analysis
The examination of visual images to interpret and understand their content.
Visual Communication
Visual Communication
The conveyance of ideas and information through visual aids such as images, graphs, and designs.
Color Theory
Color Theory
A set of principles used to understand how colors interact and affect each other in design.
Design Principles
Design Principles
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Composition
Composition
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Study Notes
Absolute Value Equations and Inequalities
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Absolute Value Definition: The absolute value of a number (x), written |x|, represents the undirected distance from x to 0 on a number line.
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Solving Absolute Value Equations (Case 1): To solve an equation of the form |ax + b| = k (where k > 0), solve the compound equation ax + b = k or ax + b = -k. This typically results in two solutions.
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Solving Absolute Value Inequalities (Case 2): To solve |ax + b| > k, solve the compound inequality ax + b > k or ax + b < -k. The solution set is often disjoint intervals.
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Solving Absolute Value Inequalities (Case 3): To solve |ax + b| < k, solve the three-part inequality -k < ax + b < k. The solution is a single interval. These rules also apply for greater-than-or-equal-to (≥) and less-than-or-equal-to (≤) inequalities. The solution set for inequalities often includes endpoints using brackets instead of parentheses.
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Absolute Value Properties:
- The absolute value of an expression is never negative (|a| ≥ 0).
- The absolute value of an expression is equal to zero only when the expression is zero.
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Description
This quiz covers the fundamental concepts of absolute value equations and inequalities. Learn how to solve equations of the form |ax + b| = k, as well as inequalities |ax + b| > k and |ax + b| < k. Mastering these concepts is crucial for your understanding of algebra.
