/*! 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 73 Will help you prepare for the ma... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 73

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

Short Answer

Expert verified
-1

Step by step solution

01

Rewrite the Equation

The exercise starts with the equation \(-2 x - 4 = x + 5\). In the first step, aim to get all terms with \(x\) on one side of the equation and the constants on the other side. This can be achieved by adding \(2x\) to both sides of the equation: \(x + 5 = 4\).
02

Rearranging the Equation

In the second step, continue with the goal of solving for \(x\). Subtract \(5\) from both sides of the equation to isolate \(x\): \(x = -1\).
03

Solved

The resulting equation \(x = -1\) is the solution of the given equation.

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.

Solving Linear Equations
Learning to solve equations is a fundamental skill in algebra. An equation like \(-2x - 4 = x + 5\) consists of expressions set equal to each other. The main goal when solving linear equations is to find the value of the variable that makes the equation true.

To solve any equation, remember these essential steps:
  • Identify the variable and terms on both sides of the equation.
  • Determine operations needed to simplify and group similar terms.
  • Perform steps that isolate and solve for the variable.
Each of these steps helps in systematically breaking down and reorganizing the equation for easier solving. Always keep equations balanced by performing the same operation on both sides.
Algebraic Manipulation Techniques
Algebraic manipulation involves rearranging and simplifying equations to make them easier to solve. This requires applying algebraic rules and operations:
  • Addition/Subtraction: When terms with a variable are on both sides, move them to one side by adding or subtracting entire expressions. In the example, you add \(2x\) to both sides to get \(-4 = 3x + 5\).
  • Distribution and Combining Like Terms: Simplify the equation by combining like terms or distributing to eliminate parentheses. Though not needed in our example, it's good to know for complex equations.
  • Balancing Equations: Always balance an equation by performing the same operation on both sides to maintain equality.
These techniques help rearrange equations into a simpler form, aiding in problem-solving and reducing mistakes during calculations.
Isolating the Variable
Isolating the variable is the process of manipulating the equation to get the variable by itself on one side of the equation. After algebraic manipulation has grouped similar terms together, isolation comes next:
  • Identify and move constant terms away from the variable, like subtracting \(5\) in the example.
  • Perform operations to remove any coefficients from the variable. If the variable had a coefficient other than 1, divide by that number.

This step translates the equation into a direct solution for the variable. For \(-2x - 4 = x + 5\), the isolation of \(x\) yields \(x = -1\) after proper manipulation. Making \(x\) the subject of the equation helps verify and apply solutions to problems.

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

Perform the indicated operations. Simplify the result, if possible. $$\frac{a b}{a^{2}+a b+b^{2}}+\left(\frac{a c-a d-b c+b d}{a c-a d+b c-b d} \div \frac{a^{3}-b^{3}}{a^{3}+b^{3}}\right)$$

What is a rational expression?

This will help you prepare for the material covered in the next section. Evaluate $$\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}$$ for \(a=2, b=9,\) and \(c=-5\)

Rationalize the numerator. $$\frac{\sqrt{x}-\sqrt{y}}{x^{2}-y^{2}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{2 x-1}{x-7}+\frac{3 x-1}{x-7}-\frac{5 x-2}{x-7}=0$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete 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.