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Chapter 1: Problem 67

Find the absolute value. $$|-8-2|$$

Short Answer

Expert verified
The absolute value of |-8-2| is 10.

Step by step solution

01

Addition/Subtraction

First, subtract 2 from -8. The result of this operation is -10.
02

Absolute Value

The absolute value of -10 is calculated as |-10|. Since absolute value is always positive or zero, the result is 10.

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Key Concepts

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

Addition and Subtraction in Algebra
When dealing with addition and subtraction in algebra, it's important to understand the rules that govern these operations with negative numbers. Take the expression \( |-8-2| \). Here, we face two numbers: -8 and -2.

Now let's break down the process step by step - first, we perform the subtraction. Mentally, you can think of -2 as taking away 2 from what you have. Since we're starting with -8, taking away 2 more gets us to -10. A helpful tip when subtracting negative numbers is to think of it as moving further from zero in a negative direction on a number line.
Calculating Absolute Value
The concept of calculating absolute value can be understood as finding the distance of a number from zero on the number line, without considering direction. The absolute value of a number is always non-negative, regardless of the original number's sign.

From our earlier calculation, we have -10. To find the absolute value, denoted as \( |-10| \), we look at how far -10 is from zero. The answer is '10 units away'. In algebra, this transformation from a negative to its positive counterpart is crucial for solving absolute value equations or inequalities.
Positive Numbers
The term positive numbers refers to numbers greater than zero. They are on the right side of the zero on a number line. One fundamental property of positive numbers is that they remain unchanged when taking their absolute value. This is because they are already a certain distance away from zero in the positive direction.

To make this more concrete, let's think about absolute values again. If a number is positive, like 5, its absolute value is 5, denoted as \( |5| \). This simplicity is the beauty of working with positive numbers in algebra 鈥� their absolute values are immediately clear, making them easier to handle in equations and real-world applications alike.

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