Understanding the Concept of Isolation in Algebra

Oct 13, 2025 by miodeya.com 82 views

Understanding the Concept of Isolation in Algebra

In algebra, isolation is a crucial concept that involves solving equations by isolating the variable on one side of the equation. This process requires a series of steps to manipulate the equation and ultimately find the value of the variable. However, in many cases, the solution provided may seem incomplete or incorrect, leaving the reader wondering what the missing step is. In this article, we will explore the concept of isolation in algebra and examine a specific problem to identify the missing step in the solution.

The Problem

Let's consider the following equation:

10.4x = 104

The solution provided is as follows:

A. Add 10.4 to both sides. B. Add negative 10.4 to both sides. C. Multiply both sides of the equation by 10.4. D. Divide both sides of the equation by 10.4.

Analyzing the Options

To identify the missing step in the solution, let's analyze each option:

Option A: Add 10.4 to both sides. This option is incorrect because adding 10.4 to both sides would result in 20.8x = 114.4, which is not the correct solution.
Option B: Add negative 10.4 to both sides. This option is also incorrect because adding negative 10.4 to both sides would result in 0 = -10.4, which is not the correct solution.
Option C: Multiply both sides of the equation by 10.4. This option is incorrect because multiplying both sides by 10.4 would result in 104x^2 = 1089.6, which is not the correct solution.
Option D: Divide both sides of the equation by 10.4. This option is the correct solution because dividing both sides by 10.4 would result in x = 10.

The Correct Solution

The correct solution involves dividing both sides of the equation by 10.4, which is option D. This step is necessary to isolate the variable x and find its value.

Why is Isolation Important?

Isolation is a crucial concept in algebra because it allows us to solve equations and find the value of the variable. By isolating the variable, we can determine its value and use it to solve other equations. In the context of the problem, isolation is necessary to find the value of x, which is the solution to the equation.

Conclusion

Understanding the Concept of Isolation in Algebra

Q&A: What is the Missing Step in the Solution?

Q: What is the concept of isolation in algebra? A: Isolation in algebra is the process of solving equations by isolating the variable on one side of the equation. This involves a series of steps to manipulate the equation and ultimately find the value of the variable.

Q: Why is isolation important in algebra? A: Isolation is important in algebra because it allows us to solve equations and find the value of the variable. By isolating the variable, we can determine its value and use it to solve other equations.

Q: What is the missing step in the solution to the equation 10.4x = 104? A: The missing step in the solution is to divide both sides of the equation by 10.4. This step is necessary to isolate the variable x and find its value.

Q: Why is option A (Add 10.4 to both sides) incorrect? A: Option A is incorrect because adding 10.4 to both sides would result in 20.8x = 114.4, which is not the correct solution.

Q: Why is option B (Add negative 10.4 to both sides) incorrect? A: Option B is incorrect because adding negative 10.4 to both sides would result in 0 = -10.4, which is not the correct solution.

Q: Why is option C (Multiply both sides of the equation by 10.4) incorrect? A: Option C is incorrect because multiplying both sides by 10.4 would result in 104x^2 = 1089.6, which is not the correct solution.

Q: What is the correct solution to the equation 10.4x = 104? A: The correct solution is to divide both sides of the equation by 10.4, which results in x = 10.

Q: How can I apply the concept of isolation in algebra to solve other equations? A: To apply the concept of isolation in algebra, follow these steps:

Write down the equation.
Identify the variable you want to isolate.
Use inverse operations to isolate the variable.
Simplify the equation to find the value of the variable.

Conclusion

In conclusion, the missing step in the solution is to divide both sides of the equation by 10.4. This step is necessary to isolate the variable x and find its value. By understanding the concept of isolation in algebra, we can solve equations and find the value of the variable.