Solving the Mathematical Equation: What is x if 5x55?
Equations can present a variety of challenges, and understanding how to solve them is a fundamental skill in mathematics. This article will delve into the solution of the equation 5x55. Through various methods, we will demonstrate how to systematically approach and solve such equations, providing detailed steps and explanations for clarity.
1. Introduction to the Equation
The equation in question is 5x55. At first glance, it may seem straightforward, but solving it requires a good understanding of algebraic principles.
2. Method 1: Direct Subtraction and Division
Let's consider the equation:
5x5x
Add -x to both sides to isolate the term with the variable:
5x5-xx-x
Simplify the left side:
4x50
Add -5 to both sides to further simplify:
4x5-50-5
This results in:
4x-5
Finally, divide both sides by 4 to solve for x:
x-5/4-1.25
Check:
Substituting back into the original equation:
5x5-1.255-6.255-1.25
This confirms that the solution x-1.25 is correct.
3. Method 2: Simplification and Solving
Another approach to solving the equation is to simplify it step by step:
5x55
Simplify the multiplication on the left side:
5x5/5
This simplifies to:
x1
Verification:
Substitute x1 into the original equation:
5155
The equation holds true, confirming that the solution is correct.
4. Additional Cases and Solutions
Let's explore other variations of the equation to gain a more comprehensive understanding:
Case 1: 5x0
Consider the equation:
5x0
To solve for x, divide both sides by 5:
x0/50
The solution is x0.
Case 2: 6x55
Consider the equation:
6x55
Simplify the left side:
6x5-5
This results in:
6x0
To solve for x, divide both sides by 6:
x0/60
The solution is x0.
5. Conclusion
By examining various methods of solving the equation 5x55, we have demonstrated the importance of algebraic principles in finding the solution. Whether through direct substitution, simplification, or systematic steps, the solution to the equation is x-1.25 and can be verified through substitution. Understanding these methods and principles will help in solving similar equations in the future.
Keywords: equation solving, algebraic solution, mathematical equations, variable solving, algebraic manipulation.