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Chapter 1: Problem 55

Evaluate each expression. $$|2|-|-2|+|-5|$$

Short Answer

Expert verified
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Step by step solution

01

Evaluate absolute value of 2

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, the absolute value of 2 is 2: \( |2| = 2 \)
02

Evaluate absolute value of -2

Similarly, the absolute value of \(-2\) is the distance of \(-2\) from zero on the number line, which is 2: \( |-2| = 2 \)
03

Evaluate absolute value of -5

The absolute value of \(-5\) is the distance of \(-5\) from zero on the number line, which is 5: \( |-5| = 5 \)
04

Substitute and calculate

Plug the evaluated absolute values back into the original expression and calculate: \( |2| - |-2| + | -5| = 2 - 2 + 5 \) Now perform the arithmetic operations: \( 2 - 2 + 5 = 0 + 5 = 5 \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number Line
Understanding the number line is crucial for grasping concepts like absolute values. Imagine a line where each point represents a number. To the right of zero, you'll find positive numbers, while to the left, you'll locate negative numbers. Zero is right in the middle. This visual helps you see exactly how far any number is from zero.
For example, both 2 and -2 are two units away from zero, just in different directions. To find the absolute value, you only need this distance, not the direction.
This makes the number line a simple but powerful tool for understanding the concept of distance from zero.
Arithmetic Operations
Arithmetic operations like addition and subtraction are fundamental to solving most math problems.
Let's break down the expression: \(|2| - |-2| + |-5|\).
First, evaluate each absolute value. From the number line, we see that both 2 and -2 are two units from zero: \(|2| = 2\) and \(|-2| = 2\).
\(-5\) is five units away: \(|-5| = 5\).
Substituting these values into the expression, we get: \(2 - 2 + 5\).
Next, perform the arithmetic operations step-by-step:
  • Start with \(2 - 2\): this equals 0.
  • Then add 5 to 0: this equals 5.
So, the final answer is 5.
Distance from Zero
The concept of absolute value represents a number's distance from zero on the number line.
It does not consider the direction, only the distance. Think of it as measuring how far away a number is from zero in either direction.
This makes working with absolute values straightforward. For instance:
  • \(|2|\) is 2 units from zero.
  • \(|-2|\) is also 2 units from zero.
  • \(|-5|\) is 5 units from zero.
In summary, the absolute value of any number is always positive or zero. This is because it simply measures distance, and distance can never be negative.

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