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Chapter 3: Problem 504

In the following exercises, evaluate. $$ -|-y| \text { when } y=17 $$

Short Answer

Expert verified
-17

Step by step solution

01

- Understand the Absolute Value

The absolute value of a number is the non-negative value of that number regardless of its sign. For any number, \( |y| \), it is always positive or zero.
02

- Substitute the Value

Substitute \( y = 17 \) into the expression \( -|-y| \). This gives \( -|-17| \).
03

- Compute the Inner Absolute Value

Compute the absolute value inside the expression. Here, \( |-17| = 17 \) because the absolute value of \( -17 \) is 17.
04

- Apply the Negative Sign

Now, take the negative of the result obtained from the absolute value. This means computing \( -17 \).
05

- Final Answer

Thus, \( -|-y| \) when \( y = 17 \) results in \( -17 \).

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Key Concepts

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

absolute value
Absolute value is a fundamental concept in prealgebra. It represents the 'distance' of a number from zero on the number line, without considering direction. This means the absolute value of a number is always non-negative, regardless of whether the original number was positive or negative.
For instance, if we consider the number -17, its absolute value is written as \( |-17| \). This means looking at the distance of -17 from zero, which is 17 units. Hence, \( |-17| = 17 \). Similarly, \( |17| = 17 \) as well.
Recognizing this property helps in various calculations, particularly when evaluating expressions involving absolute values.
negative numbers
Negative numbers are those less than zero, represented with a minus sign (鈭�). They appear frequently in various math problems and practical scenarios. When working with negative numbers and absolute values, it's crucial to distinguish between them.
For example, let's analyze \( -y \) where \( y = 17 \). Here, \( -y = -17 \). When taking the absolute value, you get \( |-17| \), which translates back to 17. However, notice when you put the negative sign after the absolute value, you reverse it back to \( -|-17| = -17 \).
This back and forth shows the importance of understanding the role of the negative sign and absolute value in different contexts.
evaluating expressions
Evaluating expressions involves simplifying them down to a single value by following mathematical rules. Let鈥檚 break it down using the example \( -|-y| \) when \( y = 17 \).
  • Step 1: Understand that \( |-y| \) means you first take the absolute value of the negative number.
  • Step 2: Replace \( y \) with 17 in the expression, so you have \( -|-17| \).
  • Step 3: Compute the absolute value inside which gives \( |-17| = 17 \).
  • Step 4: Apply the negative sign outside, resulting in \( -17 \).
Following these steps precisely helps in solving these kinds of problems accurately, making them easier to handle in prealgebra and beyond.

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