/*! 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 47 Add. See Examples 1 through 12,1... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 47

Add. See Examples 1 through 12,18, and 19. $$ |5+(-10)| $$

Short Answer

Expert verified
The result is 5.

Step by step solution

01

Evaluate the Expression Inside the Absolute Value

First, calculate the expression inside the absolute value bars. Here, we have:\(5 + (-10) = 5 - 10\).Subtract 10 from 5, resulting in \(-5\).
02

Apply the Absolute Value

Next, apply the absolute value to \(-5\). The absolute value function makes any negative number positive. Therefore:\(|-5| = 5\).

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.

Evaluating Expressions
When working with mathematical expressions, the goal is to simplify them to a single value. Evaluating an expression inside absolute value bars means performing operations in the correct order. This means handling any additions, subtractions, multiplications, or divisions first, before addressing the absolute value itself.
  • Start with any operations inside parentheses or absolute value bars.
  • Follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
  • Once all operations are completed, if there's an absolute value, convert the final number within the bars to a positive.
In our example, we first consider the expression inside the absolute value: \(5 + (-10)\). This simplifies the expression by recognizing and solving the addition of opposite integers first, so it becomes \(-5\). Once evaluated, we then apply the absolute value rule by making \(-5\) a positive \(5\).
Integer Operations
Integer operations are foundational in mathematics and involve calculations with whole numbers, which can be positive or negative. Understanding these operations helps in simplifying complex expressions.
  • Adding positive integers increases the value.
  • Adding a negative integer is equivalent to subtraction.
  • Subtracting a negative integer is like adding a positive one.
In the expression \(5 + (-10)\), we treat the negative sign in front of 10 as a signal to subtract. This transforms our problem into a straightforward subtraction: \(5 - 10 = -5\). Understanding integer rules makes operations with positives and negatives straightforward and intuitive.
Subtraction
Subtraction is the arithmetic operation of finding the difference between numbers. It involves reducing or taking away one number from another. Negative and positive numbers interact a bit differently during subtraction from what we might consider 'normal' subtraction.
  • When subtracting a larger number from a smaller one, the result is negative.
  • When subtracting a smaller number from a larger one, the result is positive.
  • Subtracting two identical numbers results in zero.
For example, in \(5 - 10\), because 10 is larger than 5, we conclude that the answer will be negative, specifically \(-5\). Remembering this relationship is essential in evaluating differences correctly, especially when handling absolute value problems.

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

Subtract. \(-6-4\)

The highest point in Africa is Mt. Kilimanjaro, Tanzania, at an elevation of 19,340 feet. The lowest point is Lake Assal, Djibouti, at 512 feet below sea level. How much higher is Mt. Kilimanjaro than Lake Assal? (Source: National Geographic Society)

Simplify each expression. \(|-3|+2^{2}+[-4-(-6)]\)

Subtract. \(3-(-6)\)

Subtract. \(-\frac{4}{7}-\left(-\frac{1}{7}\right)\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Decision 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.