/*! 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 69 Combine like terms. \(5 a+(-8 ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 69

Combine like terms. \(5 a+(-8 a)\)

Short Answer

Expert verified
-3a

Step by step solution

01

- Identify the terms

Identify the like terms in the given expression: In this case, the terms are both involving the variable 'a': 5a and -8a.
02

- Combine the coefficients

Add the coefficients of like terms together: Here, you have 5 and -8. So, calculate 5 + (-8).
03

- Simplify the expression

Perform the addition: 5 + (-8) = -3. Therefore, the combined term is -3a.

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.

Algebraic Expressions
An algebraic expression is a combination of constants, variables, and operators such as addition, subtraction, multiplication, and division. For instance, in our exercise, we see the expression: 5a + (-8a).
- **Constants** are fixed values, like 5 or -8.
- **Variables** are symbols that represent numbers, in this case, 'a'.
The goal when dealing with algebraic expressions often involves simplifying or solving them to find the value of the variable. Understanding the components of an algebraic expression helps in effectively combining like terms.
Coefficients
Coefficients are the numerical part of terms that multiply the variable. In the given exercise, 5 is the coefficient of 'a' in 5a, and -8 is the coefficient of 'a' in -8a.
- Coefficients can be positive or negative.
- They dictate how many times the variable is multiplied.
When combining like terms, you are essentially summing the coefficients. In our worked example: Combining 5 (coefficient of the first term) and -8 (coefficient of the second term) gives us -3. The resulting term is -3a.
Simplifying Expressions
Simplifying an algebraic expression means reducing it to its simplest form. This involves
- Combining like terms.
- Performing arithmetic operations such as addition or subtraction.
Using our exercise, to simplify 5a + (-8a), we
1. Identify that both terms are like terms because they both involve 'a'.
2. Combine their coefficients: 5 + (-8), which equals -3.
Thus, the simplified expression is -3a.
Simplifying expressions makes them easier to understand and work with in further calculations.

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

Translate to an algebraic expression.[ 1.1] Nine more than twice a number

If \(n>0, m>0,\) and \(n \neq m,\) classify each of the following as either true or false. $$ m-n=-(n-m) $$

Simplify. Match the algebraic expression with the equivalent rewritten expression below. Check your answer by calculating the expression by hand and by using a calculator. A) \((5(3-7)+4 \wedge 3) /(-2-3)^{2}\) B) \((5(3-7)+4 \wedge 3) /\left(-2-3^{2}\right)\) C)\((5(3-7)+4) \wedge 3 /-2-3^{2}\) D) \(5(3-7)+4 \wedge 3 /(-2-3)^{2}\) $$ \frac{5(3-7)+4^{3}}{(-2-3)^{2}} $$

Evaluate. $$ 50 \div 2 \cdot t, \text { for } t=-5 $$

SYNTHESIS Is it true that for all real numbers \(a, b,\) and \(c\) $$ a|b-c|=a b-a c ? $$ Why or why not?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics 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.