Solving Linear Equations: A Step-by-Step Guide with 2x - 5 15 Example

Linear equations are a fundamental part of algebra, and mastering them is crucial for students and professionals in math, science, and engineering. This article will guide you through solving a specific linear equation: 2x - 5 15.

Example Problem and Solution

Let's start with the equation 2x - 5 15.

Step 1: Add 5 to both sides of the equation to isolate the term with the variable on one side.

2x - 5 5 15 5

2x 20

Step 2: Divide both sides by the coefficient of x (which is 2 in this case) to solve for x.

2x / 2 20 / 2

x 10

Alternative Solution Methods

Here are alternative ways to solve the same problem, along with explanations:

Mental Math Style

1. Subtract 5 from both sides:

2x - 5 15

2x 15 5

2x 20

2. Divide both sides by 2:

2x / 2 20 / 2

x 10

Algebraic Steps

1. Subtract 5 from both sides:

2x - 5 15

2x - 5 5 15 5

2x 20

2. Divide both sides by 2:

2x / 2 20 / 2

x 10

Verification: Substitute x 10 back into the original equation:

2(10) - 5 15

20 - 5 15

15 15

Concept of Linear Equations

A linear equation in one variable can be expressed in the form:

ax b c

Where a, b, and c are constants, and x is the variable.

There are three general steps to solving such equations:

1. Isolate the variable term on one side of the equation using addition or subtraction.

2. Simplify the equation by performing the same operations on both sides.

3. Isolate the variable by dividing both sides by the coefficient of the variable.

Note: The key principle is to ensure that the same operations are applied to both sides of the equation to maintain equality.

Conclusion

Solving linear equations such as 2x - 5 15 is a fundamental skill in algebra. By following the detailed steps and alternative methods provided in this article, you can solve similar equations efficiently and accurately.

Mastering these techniques will not only help you in academic settings but also in various real-world applications where linear equations are used, such as in physics, economics, and engineering.

If you have any questions or need further clarification, feel free to comment below or contact a tutor or teacher. Happy solving!