/*! 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 77 Perform each indicated operation... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 77

Perform each indicated operation. $$ |-5-6|+|9+2| $$

Short Answer

Expert verified
22

Step by step solution

01

- Simplify inside the absolute value

Evaluate the expressions inside the absolute value bars: \[ |-5-6| \text{ and } |9+2| \]
02

- Perform each operation

Perform the subtraction and addition inside the absolute values: \[ |-5-6| = |-11| \]\[ |9+2| = |11| \]
03

- Apply the absolute value

Convert the results to their absolute values: \[ |-11| \rightarrow 11 \]\[ |11| \rightarrow 11 \]
04

- Add the results

Add the absolute values obtained: \[ 11 + 11 = 22 \]

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.

Subtracting Integers
When you subtract integers, it's important to remember that subtracting is similar to adding the opposite. For instance, a simple example would be subtracting 5 from -5, written as -5 - 6. In this case:
  • -5 is the first integer.
  • The subtraction sign indicates that you need to take away.
  • 6 is the number to be subtracted.

Subtracting 6 from -5 is the same as adding -6 to -5. So, you can rewrite -5 - 6 as -5 + (-6).
To solve this:
  • Combine -5 and -6.
  • This equals -11, since two negatives combined will give a larger negative number.

This makes our original problem easier.Understanding how to handle negative numbers and subtraction is key.
Adding Integers
Adding integers follows straightforward rules:
  • When you add two positive numbers, you get a bigger positive number. For instance, 9 + 2 = 11.
  • When adding two negative numbers, the result is more negative. For example, -5 + (-6) = -11.
  • Adding a positive number to a negative number (or vice versa) decreases the value of the larger absolute number. For instance, -5 + 11 = 6 because 11 is larger in magnitude than 5, resulting in a positive number.

In our problem, adding 9 and 2 is straightforward because both numbers are positive:
  • 9 is positive.
  • 2 is positive.
  • Adding these gives us 11.

Simple addition helps set up for the next step: applying absolute values.
Applying Absolute Value
Absolute value refers to a number's distance from zero on the number line, regardless of direction. It is always non-negative.
In our problem, we need to apply the absolute value to two results:
  • The result from -5 - 6, which was -11. The absolute value of -11 is written as |-11| and equals 11.
  • The result from 9 + 2, which was 11. The absolute value is written as |11| and also equals 11.

Therefore, our expression becomes othe sum of these absolute values:
  • | -11 | = 11
  • | 11 | = 11
  • Adding these gives us 11 + 11 = 22.

Understanding how to find and use absolute values is crucial. Absolute values simplify the comparison and addition of negative and positive 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

Perform each indicated operation. $$ -3+[(-5-8)-(-6+2)] $$

The two tables show the heights of some selected mountains and the depths of some selected trenches. Use the information given to answer. \( \)\begin{array}{|l|c|}\hline \text { Mountain } & {\text { Height (in feet) }} \\\ {\text { Foraker }} & {17,400} \\ {\text { Wilson }} & {14,246} \\\ {\text { Pikes Peak }} & {14,110} \\ \hline\end{array} $$ \begin{array}{|l|c|}\hline\text {} & {\text { Depth }( \text { in feet } } \\ {\text { Trench }} & {\text { as a negative number }} \\ {\text { Philippine }} & {-32,995} \\ {\text { Cayman }} & {-24,721} \\ {\text { Java }} & {-23,376} \\ \hline \end{array} $$ What is the difference between the height of Pikes Peak and the depth of the Java Trench?

Write a numerical expression for each phrase and simplify. See Examples 7 and \(8 .\) The product of 12 and the difference between 9 and \(-8\)

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

Solve each problem. Linda Des Jardines owes \(\$ 870.00\) on her MasterCard account. She returns two items costing \(\$ 35.90\) and \(\$ 150.00\) and receives credit for these on the account. Next, she makes a purchase of \(\$ 82.50\) and then two more purchases of \(\$ 10.00\) each. She makes a payment of \(\$ 500.00 .\) She then incurs a finance charge of \(\$ 37.23 .\) How much does she still owe?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics 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.