/*! 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 44 Simplify. $$ (-6 x+8 y)+(6 x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 44

Simplify. $$ (-6 x+8 y)+(6 x+2 y) $$

Short Answer

Expert verified
10y

Step by step solution

01

Identify Like Terms

Recognize the like terms in the expression. The given expression is ewlineewline(-6x + 8y) + (6x + 2y)ewlineewlineHere, -6x and 6x are like terms, and 8y and 2y are like terms.
02

Combine Like Terms

Add the like terms separately. First, combine the x-terms:ewline(-6x + 6x) = 0xewlineewlineNext, combine the y-terms:ewline(8y + 2y) = 10y
03

Simplify the Expression

Now combine the simplified terms from Step 2. Since 0x is zero, it does not need to be included in the final expression. The simplified expression is:ewline10y

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
In algebra, 'like terms' are terms that have the same variables raised to the same power. This makes them easily combinable. For example, in the expression (-6x + 8y) + (6x + 2y), the like terms are:
  • -6x and 6x
  • 8y and 2y
Recognizing like terms is crucial for simplifying algebraic expressions. Each term must have the same variable components. For instance,
  • 3x and -2x are like terms
  • 5y and y are like terms (with an implicit '1' as the coefficient)
  • 4x^2 and -x^2 are like terms
Practicing to identify like terms will make solving algebraic problems much easier!
combining like terms
Once you have identified the like terms, the next step is to combine them. Combining like terms involves adding or subtracting their coefficients. For example, in the expression: (-6x + 8y) + (6x + 2y)
We can combine:
  • -6x and 6x to get 0x
  • 8y and 2y to get 10y
Combining like terms simplifies the expression, making it easier to work with and understand. Here's a pro tip:
  • Always perform addition or subtraction of coefficients step by step.
  • Double-check to confirm that the terms being combined are indeed like terms.
  • Keep the variable part unchanged during this process.
Identifying and combining like terms accurately will ensure correct results.
simplifying expressions
Simplifying expressions means making them as clear and concise as possible. After identifying and combining like terms, simplifying the expression is the final step. For the given exercise:
The original expression is: (-6x + 8y) + (6x + 2y)
Step-by-step simplification:
  • Identify like terms: -6x and 6x, 8y and 2y
  • Combine the x-terms: -6x + 6x = 0x
  • Combine the y-terms: 8y + 2y = 10y
After combining, we get: 0x + 10y
Since 0x equals zero, it can be omitted from the expression.
Hence, the simplified expression is 10y.
Simplifying expressions helps eliminate unnecessary components, making further calculations easier. Always remember:
  • Perform operations carefully step-by-step.
  • Eliminate zero coefficients to simplify the final answer.
Practice simplifying different expressions to gain confidence and efficiency in solving algebraic equations.

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

Decide whether the given ordered pair is a solution of the given system. $$ \begin{aligned} &\begin{array}{c} {(2,-3)} \\ {x+y=-1} \end{array}\\\ &2 x+5 y=19 \end{aligned} $$

Write a system of equations for each problem, and then solve the system. A \(90 \%\) antifreeze solution is to be mixed with a \(75 \%\) solution to make \(120 \mathrm{L}\) of a \(78 \%\) solution. How many liters of the \(90 \%\) and \(75 \%\) solutions will be used? $$ \begin{array}{|c|c|c|} \hline \text { Liters of } & {\text { Percent (as }} & {\text { Liters of }} \\\ {\text { Solution }} & {\text { a decimal )}} & {\text { Pure Antifreeze }} \\\ {x} & {0.90} \\ {y} & {0.75} \\ {120} & {0.78} & {} \\ \hline \end{array} $$

Solve each system by the substitution method. Check each solution. $$ \begin{aligned} &\frac{x}{2}+\frac{y}{3}=\frac{7}{6}\\\ &\frac{x}{4}-\frac{3 y}{2}=\frac{9}{4} \end{aligned} $$

Without graphing, answer the following questions for each linear system. (a) Is the system inconsistent, are the equations dependent, or neither? (b) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? (c) Does the system have one solution, no solution, or an infinite number of solutions? $$ \begin{aligned} &2 x+3 y=12\\\ &2 x-y=4 \end{aligned} $$

Write a system of equations for each problem, and then solve the system. RAGBRAI", the Des Moines Register's Annual Great Bicycle Ride Across Iowa, is the longest and oldest touring bicycle ride in the world. Suppose a cyclist began the \(471 \mathrm{mi}\) ride on July \(20,2008,\) in western Iowa at the same time that a car traveling toward it left eastern Iowa. If the bicycle and the car met after 7.5 hr and the car traveled \(35.8 \mathrm{mph}\) faster than the bicycle, find the average rate of each.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

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.