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Chapter 1: Problem 46

Simplify by finding the absolute value. \(-|19|\)

Short Answer

Expert verified
-19

Step by step solution

01

- Understand the Absolute Value

The absolute value of a number is the distance between that number and 0 on a number line, regardless of direction. It is always non-negative. Represented as \(|a|\), where \(a\) is any number.
02

- Calculate the Absolute Value of 19

Since 19 is a positive number, its absolute value is just 19. Hence, \(|19| = 19\).
03

- Simplify the Expression

Substitute the value found from the previous step back into the expression: \(-|19|\). This gives us \(-19\).
04

- Final Simplified Form

After substituting and simplifying, the expression \(-|19|\) simplifies to \(-19\).

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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 an essential part of algebra that involves reducing a mathematical expression to its simplest form. This process often involves:
  • Performing arithmetic operations like addition, subtraction, multiplication, and division.
  • Combining like terms, which are terms that have the same variable raised to the same power.
  • Using properties of numbers, such as the distributive property, to simplify.
In the given exercise, you simplify the expression \(-|19|\) by first finding the absolute value of 19, which is 19, and then applying the negative sign to get \(-19\).
Number Line
A number line is a straight line that represents numbers as points on the line. It helps visualize concepts like absolute value, addition, subtraction, and the relative positions of numbers. Important points about the number line:
  • Zero is the central point.
  • Positive numbers are to the right of zero.
  • Negative numbers are to the left of zero.
For absolute value, we look at the distance from zero without considering direction. For example, both 19 and \(-19\) are 19 units away from zero, thus, \(|19| = 19\) and \(|-19| = 19\).
Negative Numbers
Negative numbers are numbers less than zero. They are represented with a minus sign (-) and are found to the left of zero on a number line. Key points about negative numbers:
  • They represent values less than zero.
  • When adding a negative number, it is similar to subtracting the absolute value of that number.
  • Multiplying and dividing by negative numbers follow specific rules: the product of two negative numbers is positive, while the product of a positive number and a negative number is negative.
In the exercise, \(-|19|\) simplifies to \(-19\), showing how absolute value affects negative numbers by making them positive before applying any operations.

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Most popular questions from this chapter

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(23,18,13,-4,\) and \(-8\)

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