/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 73 Decide whether each statement is... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 73

Decide whether each statement is true or false. \(-|-5| \geq-|-9|\)

Short Answer

Expert verified
True

Step by step solution

01

Understand the Absolute Value Notation

The absolute value of a number is its distance from zero on the number line, irrespective of direction. Therefore, the absolute value of any number is always non-negative.
02

Calculate the Absolute Values

Compute the absolute values of -|-5| and -|-9|. o |-5| = 5
03

Compute the Comparison

Now check if the inequality 鈥�5 is greater than or equal to 鈥�9. Clearly, -5 is greater than -9.
04

Conclusion

Since |-5| is indeed greater than |-9| This proves the original statement -|-5 鈥� |-9|+5 -|-9 is True

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

inequality comparison
Inequality comparison involves determining if one value is greater than, less than, or equal to another value. It uses symbols like 鈮�, <, >, 鈮�, and 鈮�. In our example, we are comparing -|-5| and -|-9| using 鈮�.

The steps are straightforward:
  • Compute each value separately.
  • Apply the inequality to see if the statement holds true.
For -|-5| 鈮� -|-9|:
  • First, calculate the absolute values. |-5| = 5 and |-9| = 9.
  • Then, negate these values: -|-5| = -5 and -|-9| = -9.
  • Finally, compare: -5 鈮� -9 is indeed true, so the statement is correct.
number line
A number line is a visual representation of numbers in a straight line, where each point corresponds to a number. It is a useful tool to understand the concept of absolute value and inequalities.

On a number line:
  • Values to the right are greater.
  • Values to the left are lesser.
Absolute value is the distance from zero without considering direction. For example, |-5| and |-9| are 5 and 9 units away from zero, respectively.

To visualize on the number line:
  • -5 is to the right of -9, making it greater.
  • This confirms that -|-5| 鈮� -|-9|.
integer properties
Understanding integer properties is key in solving problems involving absolute values and inequalities. Integers include whole numbers and their negatives, like -5, -9, 0, 1, and so forth.

Key properties include:
  • Absolute Value: Always non-negative because it measures distance from zero. For example, |-5| = 5.
  • Negative Integer Comparison: More negative integers are smaller in value. For example, -9 < -5.
In the provided problem, we used these properties:
  • Determine absolute values first (|-5| = 5 and |-9| = 9).
  • Negate the absolute values (-5 and -9).
  • Compare them (-5 is greater than -9).
This confirms that -|-5| 鈮� -|-9|.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A manufacturer has fixed costs of \(\$ 1000\) to produce widgets. Each widget costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the cost to make \(x\) widgets. (Hint: The cost will be the sum of the fixed cost and the cost per item times the number of items.)

Write a numerical expression for each phrase and simplify. 8 less than \(-2\)

Find each difference. $$ -7-(-5) $$

Decide whether each statement is true or false. \(|-12|<|-20|\)

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. All even integers between \(-18\) and \(4,\) inclusive
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.