Solving the Equation -15 - 3x 0: A Comprehensive Guide for SEO

Solving the Equation -15 - 3x 0: A Comprehensive Guide for SEO

Learning how to solve algebraic equations is fundamental to many areas of mathematics and has numerous practical applications. In this article, we will explore the method of solving the equation -15 - 3x 0 in detail. This guide not only provides a step-by-step solution but also explains the underlying principles. We will also discuss the importance of proper equation writing, the concept of transposition, and the practical significance of each step in the process.

Introduction to the Problem

The equation in question is:

-15 - 3x 0

This equation is a linear equation in one variable, x.

Step-by-Step Solution

To solve the equation -15 - 3x 0, we can follow these steps:

Step 1: Isolate the Variable Term

The first step is to bring the x-term to one side of the equation and the constant to the other side. We do this by adding 15 to both sides of the equation:

-15 - 3x 15 0 15

Simplifying this, we get:

-3x 15

Step 2: Solve for x

Next, we need to isolate x. To do this, we divide both sides of the equation by -3:

divdiv-3x / -3 15 / -3/div/div

Simplifying this, we get:

x -5

A Detailed Explanation

The process of solving the equation -15 - 3x 0 can be broken down further for better understanding:

1. Opening the Brackets

Consider the equation written with the equation written within brackets for clarity:

-15 - (3x) 0

Since the brackets contain a term with a negative sign, the result is negative. This can be simplified to:

-15 - 3x 0

2. Transposition

Transposition is the process of moving terms from one side of an equation to the other, which changes their signs. Here, we transpose -3x to the right side of the equation:

-15 3x

And then we solve for x by dividing both sides by 3:

x -5

Additional Examples

Let's consider a few additional examples to solidify the concept:

Example 1: 15 - 3x 0

Solve the equation: 15 - 3x 0

Add 3x to both sides:

15 3x

Divide both sides by 3:

x 5

Example 2: -15 - 3x 0

Solve the equation: -15 - 3x 0

Add 15 to both sides:

-3x 15

Divide both sides by -3:

x -5

Example 3: -15 - 5x 0

Solve the equation: -15 - 5x 0

Add 5x to both sides:

-15 5x

Divide both sides by 5:

x -3

Conclusion

Mastering the solution to simple algebraic equations like -15 - 3x 0 not only enhances your understanding of algebra but also improves your problem-solving skills. The techniques and concepts explained here are crucial for more advanced mathematical topics. If you need further details or want to explore more, please visit my blog page for additional resources.