/*! 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 48 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 48

Determine whether each statement is true or false. $$-3>-13$$

Short Answer

Expert verified
The statement '-3 > -13' is true.

Step by step solution

01

Check the Negativity of Numbers

This step requires recognizing the sign of the numbers involved in the inequality. The numbers involved are -3 and -13, they are both negative numbers.
02

Compare The Numbers

We know that when dealing with negative numbers, the lesser the number in absolute value is the greater. So it can be seen that -3 is greater than -13.

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.

Negative Numbers
Negative numbers are numbers that are less than zero. They come with a minus sign (-) in front of them. Imagine a thermometer: positive numbers are above zero and negative numbers go below zero.
Negative numbers have some properties:
  • Adding a negative is like subtracting a positive: \(5 + (-3) = 5 - 3 = 2\)
  • Subtracting a negative is like adding: \(5 - (-3) = 5 + 3 = 8\)
  • Two negatives make a positive: \((-2) \times (-3) = 6\)
When you work with these values, remember that rules are a bit different from positive numbers. For example, when dealing with inequalities, a smaller absolute number is actually greater if it's negative.
Absolute Value
Absolute value measures how far a number is from zero, regardless of its sign. It's like asking "how big is this number?" without caring if it's positive or negative.
You denote absolute value using vertical bars: \(|x|\). So, for example:
  • \(|-7| = 7\)
  • \(|4| = 4\)
  • \(|0| = 0\)
Absolute value helps compare negative numbers. If two numbers are negative, the one with the smaller absolute value is actually more significant. That means
\(-3\) has a smaller absolute value than \(-13\), so it is greater when compared negatively.
Number Comparison
Comparing numbers is about finding out which one is larger or has more value. When it involves negative numbers, rules change a bit. Usually:
  • A big positive number is greater than a smaller positive number: \( 5 > 2 \)
  • A less negative number is greater than a more negative number: \(-3 > -13\)
To compare negative numbers, flip your thinking. A smaller-looking negative number is greater. Imagine a debt: owe \(3 is better than owing \)13.
Visualizing on a number line also helps. Numbers to the right are bigger. So, \(-3\), being less negative, is to the right of \(-13\), thus greater. Understanding these comparisons helps solve inequalities and bring clarity to problems involving negative values.

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

Perform the indicated operations. Simplify the result, if possible. $$\frac{y^{-1}-(y+2)^{-1}}{2}$$

Perform the indicated operations. $$(x-y)^{-1}+(x-y)^{-2}$$

In solving \(\sqrt{2 x-1}+2=x,\) why is it a good idea to isolate the radical term? What if we don't do this and simply square each side? Describe what happens.

What is a rational expression?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I subtracted \(\frac{3 x-5}{x-1}\) from \(\frac{x-3}{x-1}\) and obtained a constant.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.