/*! 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 138 Will help you prepare for the ma... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 138

Will help you prepare for the material covered in the next section. Solve: \(-2 x-4=x+5\)

Short Answer

Expert verified
The solution to the equation \(-2 x-4=x+5\) is \(x = -3\).

Step by step solution

01

Identify the Equation

The given equation is \(-2x - 4 = x + 5\). This is a linear equation, which can be solved by isolating the variable 'x'.
02

Group Like Terms

Combine 'x' terms on one side of the equation and numbers on the other side. First, add '2x' to both sides of the equation to move all 'x' terms to the right side. This results in \(-4 = 3x + 5\).
03

Solve for 'x'

Next, subtract '5' from both sides to isolate 'x'. This gives \(-9 = 3x\). Dividing both sides by '3' gives the solution \(x = -3\).

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.

Understanding Linear Equations
In mathematics, linear equations form the foundation for understanding various aspects of algebra and are often one of the first types of equations we learn to solve. A linear equation is a statement of equality that contains one or two variables and does not involve any exponents or powers greater than one. The standard form of a linear equation in one variable is expressed as \(ax + b = 0\), where \(a\) and \(b\) are constants.

For example, the equation given in the exercise, \(-2x - 4 = x + 5\), represents a linear equation since the variable \(x\) does not have any exponent and the equation is in the first degree. The simplicity of linear equations allows us to perform algebraic operations to solve for the unknown variable.
Isolate the Variable
The process of finding the value of the variable that makes the equation true is known as 'isolating the variable'. To isolate the variable, we perform operations that will 'und-do' anything that is being done to the variable.

For the exercise equation, \(-2x - 4 = x + 5\), the goal is to get \(x\) on one side of the equation by itself. To do this, we need to eliminate the \(x\) terms from one side and move the constants to the other. This involves basic arithmetic operations that you already know: addition, subtraction, multiplication, and division. Once the variable is isolated, the equation is considered 'solved', which means we have found the value for the variable that balances the equation.
Combining Like Terms
Combining like terms is an essential step in simplifying algebraic expressions and equations. 'Like terms' are terms that contain the same variables to the same power. In simpler terms, they 'look' the same.

In our example, \(-2x - 4 = x + 5\), the like terms are the terms that contain \(x\). To combine them, we rearrange the equation so that all the \(x\) terms are on one side and the constant terms are on the other. By adding \(2x\) to both sides, we effectively combine the \(x\) terms, leading to \(-4 = 3x + 5\). The constants \(-4\) and \(+5\) are not like terms with \(x\), so we deal with them separately.

Mastery of combining like terms will lead to greatly simplified equations, making it easier to isolate the variable and find the solution.

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

Explaining the Concepts. Describe how to solve an absolute value inequality involving the symbol \(>.\) Give an example.

List all numbers that must be excluded from the domain of each rational expression. $$ \frac{3}{2 x^{2}+4 x-9} $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I obtained \(-17\) for the discriminant, so there are two imaginary irrational solutions.

In Exercises 95鈥�102, use interval notation to represent all values of x satisfying the given conditions. \(y=2 x-11+3(x+2)\) and \(y\) is at most 0

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ (-\infty, 3) \cup(-\infty,-2)=(-\infty,-2) $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.