/*! 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 96 Write each statement with the in... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 96

Write each statement with the inequality symbol reversed while keeping the same meaning. $$ 4.1 \leq 5.3 $$

Short Answer

Expert verified
5.3 \( \geq \) 4.1.

Step by step solution

01

Understand Inequality Direction

In the given inequality, the symbol \( \leq \) means 'less than or equal to.'
02

Identify Reversed Symbol

The reversed symbol for \( \leq \) is \( \geq \), which means 'greater than or equal to.'
03

Rewrite the Inequality

Switch the places of 4.1 and 5.3, and use the reversed symbol: 5.3 \( \geq \) 4.1.

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 symbols
Inequality symbols are used in mathematics to compare two values without using an equality sign. The most common inequality symbols are:
  • \(( < )\) which means 'less than'
  • \(( > )\) which means 'greater than'
  • \(( \leq )\) which means 'less than or equal to'
  • \(( \geq )\) which means 'greater than or equal to'
The direction of the symbol indicates the relationship between the two values. For example, the symbol \(<\) points to the smaller value. If you reverse an inequality symbol, you must also switch the positions of the two values to maintain the same meaning. This ensures that the original relationship between the values is preserved.
less than or equal to
The symbol \(( \leq )\) stands for 'less than or equal to.' This means that the value on the left side of the symbol is either smaller than the value on the right side or exactly equal to it. For instance, consider the inequality:

$$4.1 \leq 5.3$$

This tells us that 4.1 is less than 5.3 or, in a special case, it can be exactly equal to 5.3, even though it is not in this particular case. If you need to reverse this inequality, the symbol \(( \leq )\) would change to \(( \geq )\) because this is the opposite comparison.
greater than or equal to
The symbol \(( \geq )\) means 'greater than or equal to.' This indicates that the value on the left side is either greater than the value on the right side or equal to it. For example, let's reverse the inequality \(( 4.1 \leq 5.3 )\) from our exercise.

First, swap the values to reverse the positions:

$$5.3\$$ is now on the left side and $$4.1\$$ is on the right side.

Next, switch the inequality symbol \(( \leq )\) to \(( \geq )\).

The new inequality becomes:

$$5.3 \geq 4.1$$

This new statement confirms that 5.3 is indeed greater than or equal to 4.1. By switching both the symbol and the values, we retain the original meaning of the relationship between the 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

In September, Jeffery Cooper began with a checking account balance of 904.89 Dollar. His checks and deposits for September are as follows: $$ \begin{array}{|l|c|} \hline \text { Checks } & \text { Deposits } \\ \$ 41.29 & \$ 80.59 \\ \$ 13.66 & \$ 276.13 \\ \$ 84.40 & \\ \hline \end{array} $$ Assuming no other transactions, what was his account balance at the end of September?

Perform each indicated operation. $$ (8-1)-12 $$

Write a numerical expression for each phrase and simplify. See Examples 7 and \(8 .\) The product of \(-3\) and the difference between 3 and \(-7\)

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

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. \(-17,34,9,-2\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete 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.