/*! 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 49 Simplify each algebraic expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 49

Simplify each algebraic expression. $$11 a-3 a$$

Short Answer

Expert verified
The simplified form of the expression '11a - 3a' is '8a'.

Step by step solution

01

Identify Like Terms

In the expression, '11a' and '-3a' are like terms because they both contain the variable 'a' raised to the same power of '1'.
02

Combine Like Terms

The like terms can be combined by adding or subtracting them. In this case, as the expression is '11a - 3a', subtract '3a' from '11a'. This results in '8a'.

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.

Like Terms
Understanding like terms is crucial in working with algebraic expressions. **Like terms** are terms that contain the same variable raised to the same power. For example, in the expression \(11a - 3a\), both terms include the variable \(a\) raised to the power of 1, thus they are like terms.
Recognizing like terms allows us to simplify algebraic expressions by combining them efficiently.
Terms can be added or subtracted from each other only if they are like terms.
Remember:
  • Check for the same variable.
  • Ensure the variable is raised to the same exponent.
Practicing the identification of like terms will improve your ability to simplify complex expressions.
Simplifying Expressions
**Simplifying expressions** involves reducing an algebraic expression to its simplest form. This means combining like terms and performing basic mathematical operations.
In the context of our example, \(11a - 3a\), we simplify by identifying the like terms first, which are \(11a\) and \(-3a\). We then subtract \(3a\) from \(11a\) to get \(8a\).
Key steps to follow when simplifying:
  • Identify and group together like terms.
  • Perform addition or subtraction on the coefficients while keeping the variable unchanged.
Simplifying expressions is a foundational skill in algebra, making further algebraic manipulations easier.
Variables in Algebra
**Variables** are a central component in algebra. They are symbols, usually letters like \(a, b, x, y\), which represent unknown or changeable numbers.
When we refer to variables, we indicate that particular quantities could vary or are yet to be determined.
In expressions like \(11a - 3a\), \(a\) is a variable. Understanding variables is essential because:
  • They allow flexibility in representing general algebraic relationships.
  • They make it easier to express mathematical equations and formulas.
  • We can perform different operations using variables, as seen when simplifying expressions.
Grasping the concept of variables enables you to tackle a wide range of algebra problems 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

Without using a number line, describe how to add two numbers with the same sign. Give an example.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The algebraic expression \(\frac{6 x+6}{x+1}\) cannot have the same value when two different replacements are made for \(x\) such as \(x=-3\) and \(x=2\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. The rules for the order of operations avoid the confusion of obtaining different results when I simplify the same expression.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(24 \div 6) \div 2=24 \div(6 \div 2)$$

Explain how to determine the sign of a product that involves more than two numbers.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.