/*! 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 83 \((5 y+6)-(3+4 y)=10\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 83

\((5 y+6)-(3+4 y)=10\)

Short Answer

Expert verified
The solution to the equation is y = 7.

Step by step solution

01

Distribute the terms inside the parenthesis

Expand the equation by removing the parenthesis: (5y + 6) - (3 + 4y) = 10
02

Simplify the equation

Combine like terms:5y + 6 - 3 - 4y = 10Then, by combining the like terms, it is simplified to:(5y - 4y) + (6 - 3) = 10Which simplifies further to:y + 3 = 10
03

Isolate the variable y

Subtract 3 from both sides to solve for y:y + 3 - 3 = 10 - 3So, now we have:y = 7

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.

Distributing Terms
When solving linear equations, the first step often involves distributing terms. This process means removing parentheses by applying the distributive property of multiplication over addition or subtraction. In our exercise, we have the equation: (5y + 6) - (3 + 4y) = 10 To distribute the terms correctly, expand the equation by removing the parentheses. Be cautious with the minus sign before the second parenthesis: 5y + 6 - 3 - 4y = 10 Notice how the minus sign affects each term inside the parentheses. In this way, you correctly distribute and simplify the expression.
Combining Like Terms
After distributing terms, the next step is to combine like terms. Like terms are terms whose variables (and their exponents) are the same. In the equation: 5y + 6 - 3 - 4y = 10 We identify the like terms. The terms with 'y' are like terms, and the constant terms (numbers without variables) are like terms: 5y and -4y; 6 and -3 Combine them to simplify further: (5y - 4y) + (6 - 3) = 10 This reduces to: y + 3 = 10 Combining like terms helps to simplify the equation into an easier form to solve.
Isolating Variables
The final step in solving linear equations is isolating the variable. Isolating the variable means getting the variable by itself on one side of the equation. In our example, we have already simplified the equation to: y + 3 = 10 To isolate 'y', we need to remove the '+ 3'. We do this by performing the opposite operation, which is subtraction in this case: y + 3 - 3 = 10 - 3 This simplifies to: y = 7 Now, the variable 'y' is isolated, and we have found its value. Isolating variables is a crucial step in solving any equation as it reveals the value of the unknown.

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

Find the measure of an angle whose supplement measures \(39^{\circ}\) more than twice its complement.

The sum of the measures of the angles of any triangle is \(180^{\circ} .\) In triangle \(A B C\), angles \(A\) and \(B\) have the same measure, while the measure of angle \(C\) is \(60^{\circ}\) greater than each of angles \(A\) and \(B\). What are the measures of the three angles?

Find two consecutive even integers such that the lesser added to three times the greater gives a sum of \(46 .\)

If five times the lesser of two consecutive integers is added to three times the greater, the result is \(59 .\) Find the integers.

Norway earned 39 medals at the 2018 Winter Olympics. The number of gold medals earned was the same as the number of silver medals. The number of bronze medals earned was 3 fewer than the number of silver medals. How many of each kind of medal did Norway earn? (Data from The Gazette.)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Pure 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.