/*! 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 49 \(5.6 x+2=4.6 x\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 49

\(5.6 x+2=4.6 x\)

Short Answer

Expert verified
x = -2

Step by step solution

01

- Move variables to one side

First, subtract 4.6x from both sides of the equation to get all terms with x on one side: \[ 5.6x + 2 - 4.6x = 4.6x - 4.6x \]Simplifying this, we have:\[ 1.0x + 2 = 0 \]
02

- Isolate the variable

Next, subtract 2 from both sides to isolate x:\[ 1.0x + 2 - 2 = 0 - 2 \]Which simplifies to:\[ 1.0x = -2 \]
03

- Solve for x

Finally, divide both sides by 1.0 to solve for x: \[ x = \frac{-2}{1.0} \]So, we have:\[ x = -2 \]

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 solving linear equations, one fundamental step is isolating the variable you're solving for.
This means getting the variable on one side of the equation and everything else on the other side.
To achieve this, you use basic arithmetic operations like addition, subtraction, multiplication, and division.

In the example equation we worked on:
  1. First, we subtracted 4.6x from both sides, which helped gather all terms with the variable x on one side.
    Mathematically, it looked like this:
    5.6x + 2 - 4.6x = 4.6x - 4.6x
    1.0x + 2 = 0
  2. Next, we subtracted 2 from both sides to further isolate x:
    1.0x + 2 - 2 = 0 - 2
    1.0x = -2
After these steps, the variable x stands alone on one side of the equation, making it easy to solve.
Simplifying Equations
Simplifying equations is another crucial part of the process. This involves combining like terms and reducing the equation to its most basic form.
Simplification helps in making the problem more straightforward and manageable.

Here鈥檚 how we simplified our example:
  1. First, we combined like terms on the left side:
    5.6x - 4.6x + 2 = 1.0x + 2
  2. Next, we got rid of the constant term on the left side by subtracting it from both sides:
    1.0x + 2 - 2 = -2
Each step of simplification brought us a step closer to isolating the variable and solving the equation.
Algebraic Manipulation
Algebraic manipulation involves using arithmetic operations to both sides of the equation to isolate the variable and solve the equation.
Tasks such as moving terms from one side to the other and factoring are common

In our example, we applied algebraic manipulation by:
  1. Subtracting 4.6x from both sides to consolidate the x terms:
    5.6x + 2 - 4.6x = 4.6x - 4.6x
    1.0x + 2 = 0
  2. Next, we eliminated the constant term on the side with the variable:
    1.0x + 2 - 2 = 0 - 2
    1.0x = -2
  3. Finally, we divided both sides by 1.0 to solve for x:
    x = -2
Mastering these algebraic manipulations makes solving linear equations easier and quicker.

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

During the 115 th session, the total number of Democrats and Republicans in the U.S. House of Representatives was \(434 .\) There were 46 more Republicans than Democrats. How many members of each party were there? (Data from www.house.gov)

If the sum of three consecutive even integers is \(60,\) what is the first of the three even integers? (Hint: If \(x\) and \(x+2\) represent the first two consecutive even integers, how would we represent the third consecutive even integer?)

Find the measure of an angle whose complement is five times its measure.

If 4 is added to twice a number and this sum is multiplied by \(2,\) the result is the same as if the number is multiplied by 3 and 4 is added to the product. What is the number?

The difference of a number and 11 is \(-31 .\) What is the number?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

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.