/*! 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 59 Find each absolute value and sim... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 59

Find each absolute value and simplify if needed. $$ |-1|+|-2|-|-3| $$

Short Answer

Expert verified
The simplified expression is 2.

Step by step solution

01

Identify Absolute Values

First, identify the absolute values within the expression \(|-1|+|-2|-|-3|\). The absolute value of a number is its distance from zero on the number line, regardless of direction. This means it is always non-negative.
02

Calculate Absolute Values

\(|-1|\) = 1, because -1 is 1 unit away from zero. \(|-2|\) = 2, because -2 is 2 units away from zero. \(|-3|\) = 3, because -3 is 3 units away from zero.
03

Simplify the Inner Expression

Now simplify the expression inside the absolute value symbols: \(|-2|-|-3|\). This translates to: 2 - 3 = -1. So, \(|-2|-|-3|\) = |-1|.
04

Calculate the Absolute Value Again

Next, find the absolute value of -1, which is 1. Therefore, \(|-2|-|-3| = |-1| = 1 \).
05

Add the Absolute Values

Finally, add the absolute values obtained: \(|-1|+1 = 1+1 = 2\).

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 operations
Absolute values tell us how far a number is from zero, without worrying about direction. Think of it as measuring the distance on a number line. So, whether the number is positive or negative, its absolute value is always positive. When we see the notation \(|-1|\), it means we want to know how far -1 is from 0. Since -1 is one unit away from zero, \(|-1| = 1\).

Applying the same logic:
  • \(|-2| = 2\)
  • \(|-3| = 3\)

Remember, absolute value operations are straightforward once you grasp they always result in non-negative numbers.
step-by-step problem solving
Solving problems step-by-step helps simplify complex operations. Follow these steps to solve the given problem: \(|-1| + |-2| - |-3|\). Breaking it down: First, identify the absolute values:
  • \(|-1|\) = 1
  • \(|-2|\) = 2
  • \(|-3|\) = 3

Next, let's simplify the expression inside the absolute value symbols: \(|-2| - |-3| = 2 - 3 = -1\).
Now, find the absolute value of -1, which is \(|-1| = 1\).
Finally, add the absolute values: \(|-1| + 1 = 1 + 1 = 2\).
Tackle each part carefully, ensuring each calculation is correct. This way, you avoid mistakes and better understand every step.
simplifying expressions
Simplifying expressions involves breaking down complex equations into more manageable parts. For example, in the expression \(|-1| + |-2| - |-3|\), identifying absolute values first simplifies our task. Here鈥檚 the step-by-step breakdown:
  • Find absolute values: \(|-1| = 1, |-2| = 2, |-3| = 3\).
  • Combine the inner expressions: \(|-2| - |-3| = 2 - 3 = -1\).
  • Apply the absolute value again: \(|-1| = 1\).
  • Add the results: \(|-1| + 1 = 2\).

Remember, simplify the expression step-by-step, ensuring each part is calculated accurately. Breaking down complex expressions makes them less intimidating and easier to handle.

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

Evaluate each expression for \(a=-3, b=64,\) and \(c=6 .\) $$ 3 a+\sqrt{b} $$

Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. See Example 11. $$ \frac{5}{9} $$

Evaluate each expression for \(a=-3, b=64,\) and \(c=6 .\) $$ \frac{2 c+a^{3}}{4 b+6 a} $$

Evaluate each expression for \(a=-3, b=64,\) and \(c=6 .\) $$ -3 a^{4}-3 c $$

Find each square root. If it is not a real number, say so. $$ \sqrt{-121} $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.