/*! 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 328 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 328

In the following exercises, solve each equation. $$ 4 y-8=16 $$

Short Answer

Expert verified
y = 6

Step by step solution

01

Isolate the Variable Term

Add 8 to both sides of the equation to eliminate the constant term.
02

Simplify the Equation

Combine like terms on both sides of the equation.
03

Solve for the Variable

Divide both sides by 4 to isolate the variable, y.

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.

Isolating Variables
Isolating the variable is a crucial step in solving linear equations. The aim is to get the variable by itself on one side of the equation.
Let's consider the given example:
\[ 4y - 8 = 16 \]
Here, the variable we want to isolate is \( y \). To start, we first need to eliminate the constant term (\( -8 \)) that is on the same side as \( y \).
To do this, we add 8 to both sides of the equation:
\[ 4y - 8 + 8 = 16 + 8 \]
This simplifies to
\[ 4y = 24 \]
By eliminating the constant, we made the variable term ready for the next steps.
Combining Like Terms
Combining like terms means simplifying expressions by adding or subtracting terms that have the same variable.
In our equation,
\[ 4y - 8 + 8 = 16 + 8 \]
We combined the constants (\( -8 \) and \( +8 \)) on the left side, which effectively cancel each other out, leaving us with
\[ 4y = 24 \]
On the right side, combining the constants (16 and 8) gives us 24.
By simplifying in this manner, we keep our equation balanced and make further steps easier to perform.
Dividing Both Sides of an Equation
The final step is solving for \( y \) by isolating it completely.
Since \( y \) is being multiplied by 4 in the term \( 4y \), we need to perform the opposite operation to isolate it. This means we should divide both sides of the equation by 4:
\[ \frac{4y}{4} = \frac{24}{4} \]
Simplifying both sides gives:
\[ y = 6 \]
Now, \( y \) is isolated, and we have solved the equation, finding that \( y = 6 \). By dividing both sides, we ensure the equation remains balanced, and we accurately determine the value of the variable.

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

Determine whether each number is a solution to the equation. \(3 x+5=23\) (a) 6 (b) \(\frac{23}{5}\)

In the following exercises, solve each equation. $$ \frac{11}{12}=\frac{2}{3} y $$

In the following exercises, translate into an equation and solve. The nurse reported that Tricia鈥檚 daughter had gained 4.2 pounds since her last checkup and now weighs 31.6 pounds. How much did Tricia鈥檚 daughter weigh at her last checkup?

In the following exercises, solve the equations with constants and variables on both sides. $$ 5 n-20=-7 n-80 $$

In the following exercises, translate into an algebraic equation and solve. Peter paid \(\$ 9.75\) to go to the movies, which was \(\$ 46.25\) less than he paid to go to a concert. How much did he pay for the concert?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Applied 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.