/*! 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 57 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 57

Simplify each expression. $$ \frac{2}{3} x-11+11-\frac{2}{3} x $$

Short Answer

Expert verified
0.

Step by step solution

01

Combine Like Terms

Identify and combine the like terms in the expression. In this case, the like terms are the ewline fractional constants involving the variable \(x\) and the constant terms. ewline Combine the terms involving \(x\): ewline ewline \frac{2}{3} x - \frac{2}{3} x ewline
02

Simplify Constants

Next, combine the constant terms: ewline ewline -11 + 11. ewline This combination of constants simplifies to 0.
03

Final Simplification

After combining like terms and simplifying constants, the expression becomes: ewline 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, combining like terms is an essential step for simplifying expressions. Like terms are terms that have the same variable raised to the same power. For example, in the expression \[ \frac{2}{3}x - 11 + 11 - \frac{2}{3} x \], we have two like terms with the variable \(x\): \[ \frac{2}{3} x \] and \[ -\frac{2}{3} x \.\] To combine these, we simply add or subtract their coefficients. Notice that: \[ \frac{2}{3} x - \frac{2}{3} x = 0 \]. This step helps to reduce the expression by eliminating variable terms that cancel each other out.
Simplifying Constants
Constants are numbers on their own, without any variables involved. When simplifying an expression, we combine the constants just like we combine like terms with variables. In the given problem: \[ -11 + 11 \], we see that adding \(-11\) and \(11\) results in 0. This is because -11 and 11 are opposite numbers, and their sum is zero. When simplifying expressions, always combine the constants and simplify them to get a clearer expression.
Expression Simplification
Expression simplification is the process of making an expression easier to understand and work with. After combining like terms and simplifying constants, we look at the expression to see if it can be reduced further. For the problem \[ \frac{2}{3} x - 11 + 11 - \frac{2}{3} x \], combining like terms \[ \frac{2}{3} x - \frac{2}{3} x = 0 \] and constants \[ -11 + 11 = 0 \] led us to: \[ 0. \]. This means the entire expression simplifies to zero, which indicates no further simplification is necessary. The final simplified form of the expression provides a much clearer and more concise result, which is easier to work with in any 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

Write a numerical expression for each phrase, and simplify the expression. The sum of -3 and 5 and -12

Write each expression without parentheses. $$ -(9 x+12 y) $$

Use the distributive property to rewrite each expression. $$ 5(w+4) $$

Solve each problem. In \(2000,\) the U.S. federal budget had a surplus of \(\$ 236\) billion. In \(2016,\) the federal budget had a deficit of \(\$ 616\) billion. Express the difference between these amounts as a positive number. (Data from U.S. Office of Management and Budget.)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 3 if the sum of its digits is divisible by \(3,\) and not otherwise. (a) Is 4,799,232 divisible by \(3 ?\) (b) Is 2,443,871 divisible by \(3 ?\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

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.