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Chapter 2: Problem 76

Fill in the blank with \(<,>,\) or \(=\) $$-(-4) \square-|-4|$$

Short Answer

Expert verified
4 > -4

Step by step solution

01

Understand the expressions on both sides of the blank

On the left side, there is oindent \(-(-4)\). On the right side, there is oindent\(-|鈭�4|\).
02

Simplify the left side

\(-(-4) = 4\), because the negative sign in front of the -4 makes it positive.
03

Simplify the right side

\(-|鈭�4|\). The absolute value of oindent\(-4\) is oindent \(4\), so oindent \(-|鈭�4| = -4\).
04

Compare the two sides

Comparing the two simplified values, \(4\) on the left side and \(鈭�4\) on the right side, we see that \(4 > 鈭�4\).

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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. It is always non-negative. You can think of it as taking the 'positive' version of a number.
For example:
- The absolute value of 5, denoted as \(|5| \), is 5.
- The absolute value of -5, denoted as \(|-5| \), is also 5.

In our exercise, we encountered \(|鈭�4| \), which equals 4. The absolute value helps in understanding distances and comparisons without considering direction.
negative numbers
Negative numbers are numbers less than zero. They appear on the left side of the number line.
- For example, -3, -7, and -1 are all negative numbers.

A key property of negative numbers is that multiplying or dividing two negatives gives a positive result:
- For instance, \-(-4) = 4\. Here, we flip the negative sign to get a positive number.

In our exercise, the term \(-(-4) \) simplifies to 4, as two negative signs cancel each other out.
inequalities
Inequalities are mathematical expressions showing the relationship between two values. They use symbols like <, >, <=, >=.
- For example, 3 > 2 means 3 is greater than 2.
- 1 < 4 means 1 is less than 4.

When comparing different sides in our exercise, we simplified to see \(4 \) on the left and \(-4 \) on the right, and concluded that \4 > 鈭�4.袄

This comparison shows how inequalities help us understand which numbers are larger or smaller in value.
prealgebra
Prealgebra lays the foundation for all higher-level math. It involves basic arithmetic, understanding numbers, and simple equations. Learning concepts like:

    - Absolute value: distance from zero.
    - Negative numbers: values less than zero.
    - Inequalities: comparing two values.

    For example, in our exercise, we use prealgebra skills to simplify expressions and make comparisons, like simplifying \(-(-4) \) to 4 and \(-|鈭�4| \) to -4, and then comparing them to see \4 > -4.\

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Most popular questions from this chapter

a. What number must be multiplied by \(-5\) to obtain \(-35 ?\) b. What number must be multiplied by \(-5\) to obtain \(35 ?\)

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