/*! 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 41 Solve the equation. $$4 y=-12$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 41

Solve the equation. $$4 y=-12$$

Short Answer

Expert verified
y = -3

Step by step solution

01

Identify the equation

The given equation is 4y = -12.
02

Isolate the variable

To solve for y, divide both sides of the equation by 4.
03

Perform the division

Dividing both sides of the equation 4y = -12 by 4 gives: y = -12 梅 4.
04

Simplify the result

Simplify the division to get the value of y: y = -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 the Variable
When solving linear equations, one of the most important steps is isolating the variable. In our example, we need to find the value of y in the equation 4y = -12. Our variable here is y, and we need to get y on its own on one side of the equation. This means we have to eliminate anything that's being multiplied or added to y.

To isolate the variable y, we notice that it is currently multiplied by 4. So, we will need to perform the opposite operation of multiplication to both sides of the equation.

Isolating the variable is the key step to make the equation easier to solve.
Division in Equations
After identifying that y is being multiplied by 4 in the equation 4y = -12, the next logical step is to perform division. Division is used here to undo the multiplication. We divide both sides of the equation by 4 to maintain the balance of the equation. Remember, whatever operation you perform on one side, you must perform on the other side as well.

Here's how it looks: \(4y \div 4 = -12 \div 4\)

This simplifies to: \( y = -3 \)

Division helps us break down the equation step-by-step and brings us closer to solving for y.
Simplifying Algebraic Expressions
Simplifying algebraic expressions is the process of making an equation less complex and more straightforward. In this case, after performing the division in the equation 4y = -12 (which results in y = -12 梅 4), we simplify the division result.

Here鈥檚 how:
  • Recognize that \(-12 \div 4\) simplifies to -3.
  • Thus, we get \( y = -3 \).
Simplifying the expression not only makes it easier to understand but also provides the final value of our variable. Simplification is crucial in ensuring we have the simplest form of our answer, which completes the solving 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

Apply the distributive property. $$4(x+8)$$

Apply the distributive property. $$-6(k+2)$$

Apply the distributive property. $$-2\left(13-t^{2}\right)$$

Solve the equation. $$6+z=-18$$

Solve the equation. $$-3 x+7+4 x=12$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.