Linear Equations in One Variable: Solving and Word Problems

Linear Equations in One Variable for Class 8th

Linear equations in one variable are algebraic equations that involve one variable and have a degree of one. In these equations, the highest power of the variable is one. Solving linear equations and understanding word problems involving linear equations is a crucial skill for students in 8th grade. This article will provide a detailed explanation of these concepts, focusing on solving linear equations and word problems involving linear equations.

Solving Linear Equations

To solve linear equations in one variable, you need to isolate the variable on one side of the equation. The steps to solve linear equations are as follows:

1. Step 1: Identify the variable.
2. Step 2: Identify the constant term.
3. Step 3: Choose an operation to perform to isolate the variable.
4. Step 4: Perform the operation.
5. Step 5: Check your work.

For example, consider the equation x + 5 = 10. To solve for x, follow these steps:

1. Identify the variable: x
2. Identify the constant term: 5
3. Choose an operation to perform: Subtraction
4. Perform the operation: x + 5 - 5 = 10 - 5
5. Check your work: x = 5

Word Problems Involving Linear Equations

Word problems involving linear equations require you to use the skills learned in solving linear equations. These problems typically involve real-world situations that can be described using linear equations. For example, consider the following word problem:

A bus company has an old bus that it wants to replace. The old bus has a life expectancy of 15 years, and the company wants to replace it with a new bus that has a life expectancy of 25 years. If the company wants to replace the old bus as soon as possible, how many years should it expect to operate the new bus before replacing it?

To solve this problem, we can set up a linear equation. Let x represent the number of years the company will operate the new bus before replacing it. Then, we have the following equation:

15 + x + 25 = 40

Now, we can solve for x by following the steps to solve linear equations:

1. Identify the variable: x
2. Identify the constant term: 15 + 25 = 40
3. Choose an operation to perform: Subtraction
4. Perform the operation: 40 - 15 - 25 = 0
5. Check your work: x = 0

So, the company should expect to operate the new bus for 0 years before replacing it. However, this result is not feasible, as the company cannot replace the new bus immediately after purchasing it. This highlights the importance of understanding context and making reasonable assumptions when solving word problems involving linear equations.

In conclusion, understanding linear equations in one variable and solving word problems involving linear equations is an essential skill for students in 8th grade. By following the steps to solve linear equations and making reasonable assumptions when solving word problems, students can develop a strong foundation in algebra and apply these skills to real-world situations.