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Chapter 1: Problem 49

Simplify by finding the absolute value. $$ |6-3| $$

Short Answer

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Step by step solution

01

Write the Expression

Write down the absolute value expression given in the problem: \(|6 - 3|\).
02

Simplify Inside the Absolute Value

Perform the subtraction inside the absolute value: \(6 - 3 = 3\).
03

Apply the Absolute Value

Determine the absolute value of the resulting number. The absolute value of 3 is 3 because absolute value measures the distance from zero on the number line and is always non-negative: \(|3| = 3\).

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Key Concepts

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

Simplifying Expressions
Simplifying expressions is a fundamental skill in algebra. It involves reducing a complex expression to its simplest form. In the given exercise, we started with the expression \(|6 - 3|\). To simplify this, we followed a clear set of steps. First, perform the operation inside the absolute value, which is the subtraction in this case. By rearranging the numbers and simplifying the operations, we get a more straightforward, easier-to-understand result. Simplification often helps in solving more complex algebraic problems and makes understanding the expression easier.
Absolute Value
Absolute value represents the distance of a number from zero on the number line, without considering which direction from zero the number lies. It's denoted by two vertical bars, like this: \(|x|\). The absolute value of a number is always non-negative. For example, if you have an absolute value expression \(|6 - 3|\), you perform the subtraction inside first to get 3. The absolute value of 3 is simply 3 because it's the distance from zero. Remember, the absolute value of any number is always positive or zero.
Algebraic Operations
Algebraic operations are basic mathematical operations that are often used in algebra to manipulate expressions and equations. These operations include addition, subtraction, multiplication, and division. In the exercise, we used subtraction to simplify the expression inside the absolute value brackets: \[6 - 3 = 3\]. Understanding how to perform these operations correctly is crucial because they are foundational to solving algebraic equations and simplifying expressions. Once you simplify the expression using these operations, you can apply other concepts like absolute value to get the final answer.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. The sum of \(-18\) and \(-6,\) divided by the product of 2 and \(-4\)

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