/*! 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 70 Decide whether each statement is... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 70

Decide whether each statement is true or false. $$ |-12|<|-20| $$

Short Answer

Expert verified
True

Step by step solution

01

Understand Absolute Value

Absolute value, denoted by vertical bars like \(|x|\), represents the distance of a number from zero on the number line. It is always a non-negative number. For example, \(|-5| = 5\) and \(|5| = 5\).
02

Compute Absolute Values

Find the absolute value of each number given in the inequality. \(|-12| = 12\) and \(|-20| = 20\).
03

Compare the Absolute Values

Now, compare the absolute values calculated in the previous step. We need to decide if \(12 < 20\).
04

Determine the Truth Value

Since \(12 < 20\) is a true statement, the given inequality \(|-12| < |-20|\) is also 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.

Understanding Inequality
An inequality is a mathematical statement that shows the relationship between two values when they are not equal. Instead of using an equal sign, inequalities use symbols such as <, >, 鈮�, and 鈮�. These symbols help show if one number is smaller or larger than another. In our example, we use the '<' symbol to show that one value is smaller than another. When comparing absolute values like \(|-12| < |-20|\), it helps to remember that both values should be positive before making the comparison. This can make it easier to decide if the inequality is true or false.
Using a Number Line
A number line is a visual tool that helps us understand the position and distance of numbers from zero. It runs horizontally, with zero in the middle, positive numbers to the right, and negative numbers to the left. When working with absolute values, treat both positive and negative numbers as distances from zero. For example:
  • <|12|> is 12 units away from zero.
  • <|-20|> is 20 units away from zero.
By looking at these distances, we can easily see that 12 is indeed less than 20, confirming our inequality.
Non-Negative Numbers
A non-negative number is any number that is either positive or zero. Absolute values are always non-negative because they measure distance from zero, which cannot be negative.
  • An absolute value like \(|-12| = 12\) is non-negative.
  • Even though -12 is a negative number, its absolute value is positive.
This property helps us compare absolute values without worrying about negative signs, making it easier to determine inequalities like \(|-12| < |-20|\). Always remember: when dealing with absolute values, you're only comparing non-negative numbers!

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

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. A number multiplied by \(5,\) subtracted from the sum of 14 and eight times the number

Write a numerical expression for each phrase and simplify. The product of \(-\frac{1}{2}\) and \(\frac{3}{4},\) divided by \(-\frac{2}{3}\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ (6-x)(5+y)(3+a) $$

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 8 if its last three digits form a numble by \(8,\) and not otherwise. Show that (a) \(2,923,296\) is divisible by 8 and (b) \(7,291,623\) is not divisible by 8 .

Simplify each expression. $$ 6(3 p-2)-(5 p+1) $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.