Solving the Equation: -x Equals x-50 and Understanding Its Implications

Algebra is a fundamental branch of mathematics that forms the basis for solving numerous real-world problems. One type of equation often encountered in algebra is the simple linear equation. In this article, we will explore a specific equation, -x x - 50, and understand the process of solving it. This equation, while seemingly complex at first glance, can be simplified with a few basic algebraic steps.

Understanding the Equation

The equation -x x - 50 is a linear equation where the variable x is involved. In this particular equation, we are dealing with a negative value on the left side of the equal sign and a subtraction operation on the right side. To solve this equation, we need to isolate the variable x on one side of the equation.

Step-by-Step Solution

Let's break down the solution step by step:

Combine Like Terms: The first step is to gather all terms with the variable x on one side of the equation. In this case, we need to move the x from the right side to the left side. This can be done by adding x to both sides of the equation:

-x x x - 50 x

0 2x - 50

Isolate the Variable: Now, the equation looks simpler: 2x - 50 0. To isolate x, we need to move the constant -50 to the other side. This can be achieved by adding 50 to both sides of the equation:

2x - 50 50 0 50

2x 50

Solve for x: Finally, to find the value of x, we need to divide both sides of the equation by 2:

2x / 2 50 / 2

x 25

Verification

To verify our solution, we can substitute x 25 back into the original equation:

-x x - 50

-25 25 - 50

-25 -25

This confirms that x 25 is indeed the correct solution to the equation.

Conclusion

In conclusion, the equation -x x - 50 can be solved using basic algebraic principles. By combining like terms, isolating the variable, and performing the necessary arithmetic operations, we find that the only solution to this equation is x 25. This process is not only useful in mathematics but also in various real-world applications where linear equations are prevalent.

Related Keywords

Algebra is a broad field of mathematics, and related keywords include:

Algebra Equations Solving Linear Equations Understanding Linear Functions

By exploring these related topics, one can gain a deeper understanding of algebra and its applications in various fields, from engineering to business.