/*! 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 26 Solve. $$ 3 y+4=2 $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 26

Solve. $$ 3 y+4=2 $$

Short Answer

Expert verified
y = -\frac{2}{3}

Step by step solution

01

Subtract 4 from both sides

To isolate the term with the variable on one side, subtract 4 from both sides of the equation: 3y + 4 - 4 = 2 - 4 which simplifies to 3y = -2.
02

Divide by 3

Next, divide both sides by 3 to solve for y: \( \frac{3y}{3} = \frac{-2}{3} \) which simplifies to \( y = -\frac{2}{3} \).

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
When you solve linear equations, you often need to isolate the variable to one side of the equation. This means getting the variable all by itself. To do this, you want to remove or 'undo' any other numbers or constants attached to it.
In the provided exercise, we start with the equation:
  • 3y + 4 = 2
  • The current goal is to isolate 'y' on one side.
  • To do so, you first subtract 4 from both sides to clear the constant term attached to 'y':
    3y + 4 - 4 = 2 - 4
  • This action isolates the term with the variable 'y' to one side:
  • 3y = -2
Inverse Operations
Inverse operations are used to 'undo' mathematical operations in order to isolate the variable. These are operations that 'reverse' the effect of each other.
  • For addition, the inverse operation is subtraction.
  • For multiplication, the inverse operation is division.
In our example, we used subtraction as the inverse operation to addition first.
We had to remove the '+4' by subtracting 4:
  • 3y + 4 - 4 = 2 - 4
  • This gave us:
3y = -2
  • Next, we used division as the inverse operation to multiplication to solve for y:
    \( \frac{3y}{3} = \frac{-2}{3} \)
  • Which simplifies to:
  • \( y = - \frac{2}{3} \)
Solving for Y
When solving for a specific variable, like 'y', you want to get 'y' by itself on one side of the equation.
Let鈥檚 take another look at the equation:
  • 3y + 4 = 2
  • The first action was to isolate the term with 'y':
  • 3y = -2
Next, get 'y' alone by using division:
  • \( \frac{3y}{3} = \frac{-2}{3} \)
  • This simplifies directly to:
  • \( y = - \frac{2}{3} \)
By understanding these steps and concepts, it makes it easier to solve any linear equation where you need to solve for 'y'. Learning to isolate variables, use inverse operations effectively, and understand each step deeply will strengthen your math skills enormously.

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

Jasmine is paid \(\$ 500\) per week plus \(10 \%\) of all sales she makes. a) Let \(x\) represent the amount of Jasmine's weekly sales, in dollars, and \(y\) her weekly paycheck. Write an equation expressing \(y\) in terms of \(x\) b) One week, Jasmine earned \(\$ 900 .\) What were her sales that week?

To the student and the instructor: Throughout this text selected exercises are marked with the icon Ahal. Students who pause to inspect an Ahal exercise should find the answer more readily than those who proceed mechanically. This may involve looking at an earlier exercise or example, or performing calculations in a more efficient manner. Some Ahal exercises are left unmarked to encourage students to always pause before working a problem. Evaluate each expression using the values provided. $$ x^{2}-[3(x-y)]^{2}, \text { for } x=6 \text { and } y=4 $$

Which numbers in the list provided are (a) whole numbers? (b) integers? (c) rational numbers? (d) irrational numbers? (e) real numbers?. $$ -6.08,-5,0,1, \sqrt{17}, \frac{99}{2} $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ 43-(-9+2)^{2}+18 \div 6 \cdot(-2) $$

To the student and the instructor: Writing exercises, denoted by \([\%,\) are meant to be answered using sentences. Because answers to many writing exercises will vary, solutions are not listed at the back of the book. What is the difference between rational numbers and integers?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics 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.