Problem 38 Find each sum or difference. $... [FREE SOLUTION]

Chapter 0: Problem 38

Find each sum or difference. $$ -|-5+6| $$

Short Answer

Expert verified

-1

Step by step solution

Evaluate the Absolute Value

First, find the absolute value of the expression inside the absolute value symbols: o Consider the expression o o |-5 + 6|o The absolute value of a number is its distance from zero, regardless of the direction. Since the expression inside the absolute value is -5 + 6, we first need to compute this sum.

Compute the Inside Expression

Evaluate the expression inside the absolute value: o -5 + 6 o 1. Doing the arithmetic: -5 + 6 = 1o So, the expression becomes o |1|

Remove the Absolute Value

Since the absolute value of 1 is simply 1 (as absolute value signifies the distance from zero and is always positive), we have: o |-5 + 6| = |1| = 1

Proceed with Remaining Operations

Now we have the simplified expression as: o o o -1 o -|1| o Which simplifies to: -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.

absolute value

Absolute value is a foundational concept in mathematics. It refers to the non-negative value of a number, regardless of whether the original number is positive or negative. Simply put, absolute value answers the question, 'How far is this number from zero on the number line?' The absolute value is always represented with vertical bars: $|x|$. Here's a quick guide:
- The absolute value of 5 is $|5| = 5$.
- The absolute value of -5 is $|-5| = 5$.
In the given exercise, the expression $|-5 + 6|$ involves calculating the absolute value of \-5 + 6\. First, perform the arithmetic inside the bars, which we'll dive into in the next section.

arithmetic

Arithmetic is essential for simplifying expressions, especially when working with absolute values. It includes basic operations like addition, subtraction, multiplication, and division. Let's break down the exercise step-by-step:
- Start by performing the operations inside the absolute value: $-5 + 6$.
- Adding these numbers: $-5 + 6 = 1$.
Now, the expression becomes $|1|$. This result will be useful in our final simplification step.

simplifying expressions

Simplifying expressions often involves a series of methodical steps. First, address any absolute values, as they can influence the entire expression. Using our exercise, we already transformed $|-5 + 6|$ into $|1|$. Absolute values simplify easily:

The absolute value of 1 is 1.

With the absolute value resolved, continue resolving the remaining parts of the expression. In this case:

We started with: - \ |-5 + 6|\.
This simplifies to - \ |1| = -1\.

Now you see, using concepts like absolute value, arithmetic, and simplification, you can easily manage and solve these kinds of mathematical expressions.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find each sum or difference. $$ -|-5+6| $$

Short Answer

Step by step solution

Evaluate the Absolute Value

Compute the Inside Expression

Remove the Absolute Value

Proceed with Remaining Operations

Key Concepts

absolute value

arithmetic

simplifying expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Probability and Statistics

Pure Maths

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.