/*! 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 63 Simplify it by combining any lik... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 63

Simplify it by combining any like terms. $$ 2.6 y+8.3=4.6 y-3.4 $$

Short Answer

Expert verified
The simplified solution is \( y = 5.85 \).

Step by step solution

01

Rearrange Terms with Variable 'y'

We begin by rearranging terms so that all terms containing the variable 'y' are on one side of the equation. To do this, subtract \(2.6y\) from both sides: \[2.6y - 2.6y + 8.3 = 4.6y - 2.6y - 3.4\] This simplifies to:\[8.3 = 2y - 3.4\]
02

Isolate the 'y' Term

Next, isolate the 'y' variable by moving constant terms to the other side of the equation. Add \(3.4\) to both sides of the equation:\[8.3 + 3.4 = 2y - 3.4 + 3.4\]This simplifies to:\[11.7 = 2y\]
03

Solve for 'y'

Finally, solve for 'y' by dividing both sides by 2:\[\frac{11.7}{2} = \frac{2y}{2}\]This simplifies to:\[y = 5.85\]

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.

Combining Like Terms
Combining like terms is a fundamental process in simplifying algebraic expressions and equations. It involves grouping terms that have the same variable raised to the same power. In the equation \(2.6y + 8.3 = 4.6y - 3.4\), we need to focus on the terms that contain the variable \(y\). These are \(2.6y\) and \(4.6y\). The idea is to move these terms to one side to simplify the equation further.
  • Identify like terms: In our example, \(2.6y\) and \(4.6y\) are like terms because they both contain the variable \(y\).
  • Combine them: This usually involves adding or subtracting these terms. For instance, subtracting \(2.6y\) from both sides helps to isolate the variable terms from the constants.
Combining like terms helps reduce the complexity of equations, paving the way for easier manipulation and solving.
Rearranging Equations
Rearranging equations is a technique used to organize an equation such that terms are grouped in a way that makes solving easier. It often involves moving all terms with a given variable to one side and constants to the other. In the example \(8.3 = 2y - 3.4\), rearranging allows us to effectively isolate and solve for \(y\).
  • Identify the terms you want to isolate, usually terms with the variable you aim to solve for first.
  • Move terms involving the variable to one side by adding or subtracting them from both sides. This might also involve moving constants to the opposite side.
  • Keep the equation balanced by performing the same operation on both sides.
Rearranging equations in this way prepares the equation for the next step, which is usually solving for the desired variable. This process requires careful attention to maintain equality throughout.
Solving for a Variable
Solving for a variable in an equation involves isolating the variable on one side to determine its value. After rearranging the equation \(11.7 = 2y\), we're in a position to solve for \(y\).
  • First, simplify both sides of the equation if possible.
  • Divide or multiply both sides by the coefficient of the variable to isolate it. In our case, divide both sides by 2, since \(2y\) implies \(2 \times y\).
  • The result is an expression where the variable is alone on one side, providing its value.
Solving for a variable is the culmination of steps involving simplification and rearrangement, giving you the final answer. Here it results in \(y = 5.85\), completing the solution process.

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

A shipping box can hold 36 books. If 486 books must be shipped, how many boxes are needed?

Choose the best estimate. \(8.62 \times 41.7\) a. 36 b. 32 c. 360 d. 3.6

A child is to receive a dose of 0.5 teaspoon of cough medicine every 4 to 6 hours. If the bottle contains 4 fluid ounces. If the child takes a dose every six hours, how many days will the medicine last?

Divide. \(\frac{13.49}{10}\)

Divide. Round the quotients as indicated. Divide: \(68.39 \div 0.6\). Round the quotient to the nearest tenth.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.