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Chapter 1: Problem 79

Perform each indicated operation. $$ |-8-2|-|-9-3| $$

Short Answer

Expert verified
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Step by step solution

01

Simplify inside the absolute values

First, evaluate the expressions within the absolute value brackets.\(-8-2 = -10\)and\(-9-3 = -12\).
02

Apply the absolute value

Next, apply the absolute value to each result.\(|-10| = 10\)and\(|-12| = 12\).
03

Subtract the results

Finally, perform the subtraction of the two absolute values:\(10 - 12 = -2\).

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Key Concepts

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

Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. So, the absolute value of both positive and negative numbers is always positive.
For example, the absolute value of -8 is written as \(|-8|\), which equals 8. Similarly, the absolute value of 8 is written as \(|8|\) and also equals 8.
In mathematical expressions, absolute values are denoted with vertical bars, like this: \(|x|\). These bars ask you to ignore the sign and just focus on the magnitude.
This concept is especially useful when dealing with negative numbers, where without the absolute value, operations might yield negative results.
Subtraction
Subtraction is the process of taking one number away from another. It's an essential arithmetic operation alongside addition, multiplication, and division.
In expressions like \(-8-2\), the first step is to perform the subtraction inside the parentheses. This results in \(-10\).
Similarly, for \(-9-3\), the subtraction gives \(-12\).
Subtracting involves understanding the 'difference' between numbers. While it may seem straightforward, combining this operation with absolute values can sometimes be tricky for students.
Remember, when subtracting negative numbers, you're moving left on the number line.
Evaluation of Expressions
Evaluating expressions involves simplifying them step-by-step to find their value.
Follow each operation in the correct order (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
In the given exercise, we first simplify inside the absolute values. For \(-8-2\)\, this evaluates to \(-10\). For \(-9-3\), this evaluates to \(-12\).
Next, apply the absolute value: \(|-10| = 10\) and \(|-12| = 12\).
Finally, subtract the results: \10 - 12 = -2\.
This step-by-step simplification ensures that each part of the expression is correctly handled.

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Most popular questions from this chapter

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