/*! 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 42 simplify. . $$2+5-(-3)-10$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 42

simplify. . $$2+5-(-3)-10$$

Short Answer

Expert verified
0

Step by step solution

01

Identify the Expression

The expression that needs to be simplified is: \[2 + 5 - (-3) - 10\]
02

Combine Like Terms

Break down the expression and handle each term one step at a time. Start by resolving the double negative: \[ -(-3) = +3 \]Now replace it in the expression: \[ 2 + 5 + 3 - 10 \]
03

Add and Subtract Sequentially

First, add the positive numbers together:\[ 2 + 5 = 7 \]Now add 3 to the result:\[ 7 + 3 = 10 \]Finally, subtract 10 from 10:\[ 10 - 10 = 0 \]
04

Conclusion

The simplified expression is \[ 2 + 5 - (-3) - 10 = 0 \].

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.

combining like terms
In algebra, similar types of values within an expression can be combined, which is known as 'combining like terms'. For instance, when you see numbers or variables that are alike, you can add or subtract them directly.

If we have the expression: \[ 2 + 5 - (-3) - 10 \]
You may notice that all terms are constants (plain numbers). This means we can combine them.

  • Firstly, tackle similar constants directly.
  • Perform each arithmetic operation step by step.

Combining like terms simplifies the expression and makes it easier to solve. This concept is crucial in solving more complex algebraic problems efficiently.
resolving double negatives
A double negative occurs when two negative signs are next to each other in an expression. Resolving a double negative is straightforward: two negatives make a positive.

Consider the expression: \[ 2 + 5 - (-3) - 10 \]
Here, \( -(-3) \) appears.
  • To resolve this, convert \( -(-3) \) to \( +3 \).

Rewriting the expression becomes: \[ 2 + 5 + 3 - 10 \]
This makes it easier to proceed with combining like terms and finishing the calculations. Understanding this concept helps avoid confusion and possible mistakes in your solutions.
addition and subtraction
In this concept, it is essential to follow the order of operations and perform addition and subtraction correctly. Our initial expression after resolving the double negative is: \[ 2 + 5 + 3 - 10 \]

  • First, add the positive numbers.\( 2 + 5 = 7 \)
  • Then, add \( 3 \) to the sum: \( 7 + 3 = 10 \)
  • Finally, subtract \( 10 \) from this sum: \( 10 - 10 = 0 \)

This step-by-step approach ensures accuracy. Always add and subtract sequentially, staying attentive to positive and negative signs to avoid errors. Properly managing addition and subtraction in algebra simplifies expressions effectively.

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

Rank the numbers from least to greatest. If \(b\) represents a negative number, then what is the sign of \(|b| ?\)

Perform the indicated operation. $$\frac{0}{-2}$$

Perform the indicated operation. $$\frac{0}{-5}$$

One of the most famous blizzards in the United States was the blizzard of \(1888 .\) In one part of Nebraska, the temperature plunged from \(40^{\circ} \mathrm{F}\) to \(-25^{\circ} \mathrm{F}\) in \(5 \mathrm{hr}\). What was the average change in temperature during this time?

State at least two words or phrases that would indicate subtraction.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.