Math Problem Statement

Evaluate the absolute values |−3| and |14|.

Solution

To evaluate the expressions in the image, let's break down each absolute value calculation:

  1. 3|-3|:

    • The absolute value of 3-3 is the distance from zero on a number line, which is 33.
    • Therefore, 3=3|-3| = 3.
  2. 14|14|:

    • The absolute value of 1414 is the distance from zero, which is 1414.
    • Therefore, 14=14|14| = 14.

So the answers are:

  • 3=3|-3| = 3
  • 14=14|14| = 14

Would you like further details or explanations on absolute values?

Here are some related questions to explore further:

  1. What is the definition of absolute value and how does it apply to positive and negative numbers?
  2. How does the absolute value function handle zero?
  3. Can absolute values be negative, and why or why not?
  4. What are some practical applications of absolute values in real-world scenarios?
  5. How do absolute values relate to distances on the number line?

Tip: When taking the absolute value, think of it as removing any negative sign, leaving only the "magnitude" or "distance" from zero.

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Math Problem Analysis

Mathematical Concepts

Absolute Value
Integers

Formulas

|x| = x if x >= 0; |x| = -x if x < 0

Theorems

Absolute Value Definition

Suitable Grade Level

Grades 5-7