Absolute Value Equations and Inequalities

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Questions and Answers

What is the approximate average percentage of the Earth's surface area covered by land?

  • 29%
  • 28%
  • 30% (correct)
  • 31%

Which of these has a lower density: the oceanic crust, or the continental crust?

  • They have the same density
  • Continental Crust
  • It is impossible to determine based on the information provided
  • Oceanic Crust (correct)

What is the correct order of layers, from the Earth's surface to the center?

  • Mantle, Outer core, Inner core, Crust
  • Crust, Mantle, Outer core, Inner core (correct)
  • Inner core, Outer core, Mantle, Crust
  • Crust, Inner core, Outer core, Mantle

Which part of the Earth's interior is primarily liquid?

<p>Outer core (A)</p> Signup and view all the answers

Where does most earthquake activity occur?

<p>Along the boundaries of tectonic plates (B)</p> Signup and view all the answers

Flashcards

Image Analysis

The examination of visual images to interpret and understand their content.

Visual Communication

The conveyance of ideas and information through visual aids such as images, graphs, and designs.

Color Theory

A set of principles used to understand how colors interact and affect each other in design.

Design Principles

Guidelines that help create visually appealing and effective layouts in visual communication.

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Composition

The arrangement of elements within a visual space to create a cohesive whole.

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Study Notes

Absolute Value Equations and Inequalities

  • Absolute Value Definition: The absolute value of a number (x), written |x|, represents the undirected distance from x to 0 on a number line.

  • 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.

  • 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.

  • 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.

  • 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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