/*! 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 48 Solve the equation. $$55-5 y=9... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 48

Solve the equation. $$55-5 y=9 y+27$$

Short Answer

Expert verified
The solution to the equation is \(y = 2\).

Step by step solution

01

Rearrange the Equation

Bring all terms to one side of the equation: \(55-5y = 9y+27\). This gives us the new equation \(55 - 27 = 9y + 5y\).
02

Simplify the Left and Right Side

Simplify the equation to: \(28 = 14y\).
03

Find the Value of y

Now divide both sides by 14: \(y = 28 / 14 \).

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.

Linear Equations
Linear equations are equations of the first degree, which means they have no exponent higher than one. They are usually expressed in the form \(ax + b = c\), where \(x\) is the variable to solve for, and \(a\), \(b\), and \(c\) are constants.
Linear equations have a very straightforward structure and their solutions are the point where the equation is satisfied. A real-world analogy is balancing a see-saw by adding or removing weights on either side until it is level.
The example equation, \(55-5y=9y+27\), is a linear equation with \(y\) as the variable we need to solve for.
  • Constants and Coefficients: In our exercise, we identify 55 and 27 as constants and -5 and 9 as coefficients of the variable \(y\).
  • Goal: The main goal in solving this linear equation is to find the specific value of \(y\) that makes the expression true.
Equation Rearrangement
Rearranging equations is a vital step in solving linear equations. It involves manipulating the equation to bring like terms together. The goal here is to make the equation simple enough to solve.
In our exercise, the equation \(55 - 5y = 9y + 27\) is rearranged by bringing all terms involving \(y\) to one side and constants to the other. This gives us
\(55 - 27 = 9y + 5y\).
Each side of the equation should be simplified to make the solution clearer.
  • Step One: Move all terms containing \(y\) to one side. You add \(5y\) to both sides to get all \(y\) terms together.
  • Step Two: Simplify the reduced terms on both sides. After moving the terms, subtract \(27\) from \(55\) on the left.
Rearranging simplifies the problem and sets up the next steps in finding the solution.
Algebraic Simplification
Algebraic simplification is about reducing expressions to their simplest form. It's critical when dealing with any equation to make solving easier.
After rearranging, we have the equation \(28 = 14y\). Simplification involves adding, subtracting, multiplying, or dividing terms to isolate the variable.
The simplification process includes:
  • Combining Like Terms: In this exercise, \(9y + 5y\) simplifies to \(14y\).
  • Isolating the Variable: The next step is dividing both sides by 14 to solve for \(y\). So, \(y = 28 / 14\).
This approach ultimately helps you reach the solution, which, in this case, is \(y = 2\). By understanding these simplification steps, solving even more complex equations can become much easier, fostering your algebraic skills.

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

Evaluate the expression for the given value of the variable. (Review 1.3 and 2.5 for 4.2 ) $$13-(y+2) \text { when } y=4$$

Find the x-intercept and the y-intercept of the graph of the equation. $$x+5 y=10$$

Find the \(x\) -intercept and the \(y\) -intercept of the line. Graph the equation. Label the points where the line crosses the axes. $$ 0.5 y=-2 x+8 $$

Solve the equation if possible. $$ -5 y+6=4 y+3 $$

Find the difference. $$ -\frac{2}{3}-\left(-\frac{7}{3}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

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.