Problem 25 Solve equation, and check your s... [FREE SOLUTION]

91影视

Chapter 2: Problem 25

Solve equation, and check your solution. \(4 x=-20\)

Short Answer

Expert verified

The solution is \(x = -5\).

Step by step solution

Understand the Equation

The given equation is a linear equation in the form of \(4x = -20\). To solve for \(x\), isolate the variable.

Isolate x

Divide both sides of the equation by 4 to isolate \(x\): \[4x = -20 \ \frac{4x}{4} = \frac{-20}{4} \ x = -5\]

Check the Solution

Substitute \(x = -5\) back into the original equation to ensure the solution is correct: \[4(-5) = -20 \ -20 = -20 \] Since both sides of the equation are equal, the solution \(x = -5\) is correct.

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 Equations

Solving equations is a fundamental concept in algebra. It involves finding the value of the variable that makes the equation true. In our original problem, we are given a linear equation: \(4x = -20 \). This involves finding the value of \(x\) that makes both sides of the equation equal. The first step is to understand the type of equation and then apply appropriate methods to solve it. Linear equations like this one are generally straightforward to solve because they involve simple operations such as addition, subtraction, multiplication, or division.

Isolation of Variables

To isolate the variable means to get the variable alone on one side of the equation. This often involves performing operations that cancel out other terms or coefficients. In the problem \(4x = -20\), we need to isolate \(x\). We do this by dividing both sides of the equation by 4.
\[4x = -20 \frac{4x}{4} = \frac{-20}{4} \Rightarrow x = -5 \]
By dividing both sides by the same number, we ensure that the equality is maintained, and we successfully isolate \(x\). This is a crucial step in solving equations since it simplifies the process of finding the variable's value.

Verification of Solutions

After solving an equation, it's important to verify that the solution is correct. This is done by substituting the value back into the original equation. In our problem, the solution we found is \(x = -5\). We substitute \(x = -5\) back into the original equation:
\[4(-5) = -20 \Rightarrow -20 = -20 \]
Since both sides of the equation are equal, our solution is verified to be correct. Verification ensures that no mistakes were made during the solving process and that the solution truly satisfies the original equation.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve equation, and check your solution. \(4 x=-20\)

Short Answer

Step by step solution

Understand the Equation

Isolate x

Check the Solution

Key Concepts

Solving Equations

Isolation of Variables

Verification of Solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Discrete Mathematics

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.