/*! 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 60 Find each absolute value and sim... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 60

Find each absolute value and simplify if needed. $$ |-7|+|-3|-|-10| $$

Short Answer

Expert verified
0

Step by step solution

01

Understand Absolute Value

The absolute value of a number is its distance from 0 on the number line, regardless of direction. Thus, \(|x| = x\) if \(x \geq 0\) and \(|x| = -x\) if \(x < 0\). The aim is to convert each negative number inside the absolute value symbols to its positive equivalent.
02

Apply Absolute Value to Each Term

Evaluate each absolute value term separately: \(|-7| = 7\), \(|-3| = 3\) and \(|-10| = 10\).
03

Simplify the Expression

Substitute the absolute values back into the expression and simplify: \(|-7| + |-3| - |-10| = 7 + 3 - 10 = 0\).

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
The absolute value of a number measures its distance from 0 on a number line. Distances are always positive. This means that if a number is negative, its absolute value is the positive counterpart of that number. For instance, \(-7\)'s absolute value is \(7\), because \(-7\) is 7 units away from 0. Similarly, \(-3\)'s absolute value is \(3\) and \('-10\)'s absolute value is \(10\). Absolute value is denoted using vertical bars, like this: \(|x|\). So, to solve these problems, you essentially ignore any negative sign within the absolute value symbols.
integer operations
Integer operations involve basic arithmetic with whole numbers, including positive and negative values. Key operations include addition, subtraction, multiplication, and division. In the given exercise, we first find the absolute values and then perform addition and subtraction on these values. The problem \(|-7| + |-3| - |-10|\) becomes \(7 + 3 - 10\). When adding and subtracting integers, it helps to think of movement along a number line. So 7 steps forward, another 3 steps forward, and 10 steps back results in being exactly at 0. Therefore, \(7 + 3 - 10 = 0\).
simplifying expressions
Simplifying expressions means performing all possible operations and reducing the expression to its simplest form. In the exercise, after finding the absolute values, the expression looks like this: \(|-7| + |-3| - |-10| = 7 + 3 - 10\). To simplify, start by performing addition: \(7 + 3 = 10\). Then, subtract 10 from 10: \(10 - 10 = 0\). The expression simplifies down to \(0\), which is the simplest form. Simplifying helps make complex problems easier to handle and understand.
number line
A number line is a straight line with numbers placed at equal intervals or segments along its length. It is a visual tool to understand numbers and their relationships. Positive numbers are to the right of 0, and negatives are to the left. For absolute value problems, a number line helps visualize the distance each number is from 0. For example, \(-7\) is 7 units left of 0, so its absolute value is 7. By seeing numbers as points on a line, you can better grasp operations like addition and subtraction, reinforcing the understanding that \(7 + 3 - 10\) leads back to 0 on the number line.

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

Simplify each expression. $$ -3(5)^{2}-(-2)(-8) $$

Simplify each inequality if needed. Then determine whether the statement is true or false. $$ -7<4+1 $$

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. $$ -\sqrt{900} $$

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

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision 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.