/*! 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 106 Simplify. $$ 84+(-99)+44-(-9... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 106

Simplify. $$ 84+(-99)+44-(-99)-43 $$

Short Answer

Expert verified
85

Step by step solution

01

- Simplify the sum and the differences

Identify and group together the terms with positive and negative signs. The given expression is 84 + (-99) + 44 - (-99) - 43First, change the subtraction of a negative number to adding its positive equivalent:84 + (-99) + 44 + 99 - 43
02

- Combine like terms

Now start adding and subtracting the numbers in sequence from the simplified expression. First, combine the positive integers: 84 + 44 + 99 = 227.Then, combine the negative integer:227 + (-99) = 128.Finally, subtract 43: 128 - 43 = 85.

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.

Integer Operations
When dealing with algebraic expressions, it is essential to understand integer operations. Integers include both positive and negative whole numbers. To simplify expressions, you will need to add and subtract these integers correctly.

Here are some key points to remember:
  • Adding two positive integers results in a positive sum. For instance, 5 + 6 = 11.
  • When adding two negative integers, the result is also negative. For example, -4 + (-7) = -11.
  • If you are adding a positive integer and a negative integer, subtract the smaller absolute value from the larger absolute value, and keep the sign of the number with the larger absolute value. For instance, 8 + (-3) = 5, while -10 + 4 = -6.
Understanding these basics can make algebraic simplification much more manageable.
Combining Like Terms
Combining like terms is a fundamental skill in algebra that simplifies expressions. Like terms have the same variable raised to the same power or are just constants (numbers without variables).

When you are combining like terms:
  • Group all similar terms together. For example, if you have 3x and 4x in an expression, you can group them to get 7x.
  • It is especially crucial to properly handle the coefficients (the numerical part of the terms). For instance, 2x + 3x becomes (2+3)x, which simplifies to 5x.
  • When simplifying, always pay attention to both numerical values and signs. This careful handling ensures you do not accidentally change the value of the expression.
In our given exercise, we did not technically have terms with variables, but the same principles apply when organizing and simplifying integers. Efficiently combining them reduces the expression to its simplest form.
Positive and Negative Numbers
Dealing with positive and negative numbers can sometimes be confusing, but it's crucial for algebraic simplification.

Here's how to manage them:
  • Changing the sign: When you subtract a negative number, it becomes positive (e.g., -(-3) = 3). This was used in our given exercise: 84 + (-99) + 44 - (-99) - 43 was simplified to 84 + (-99) + 44 + 99 - 43.
  • Combining positives and negatives: Get familiar with moving from simple to more complex operations by practicing basic equations and noting how signs change the results.
Practice often to become comfortable with these operations. Doing so will help you quickly simplify complex expressions.

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

Write an equivalent expression without using grouping symbols. $$ -\left(3 x^{2}+5 x-1\right) $$

Evaluate. $$ -x^{2}-5 x, \text { for } x=-3 $$

Simplify. $$ 5 x^{4}+3 x-\left(5 x^{4}+3 x\right) $$

Evaluate. $$ 9-4 x, \text { for } x=5 $$

Simplify. Jake keys \(18 / 2 \cdot 3\) into his calculator and expects the result to be \(3 .\) What mistake is he probably making?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

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.