Solving the Equation 2x5-25: A Step-by-Step Guide
Introduction to the Problem
Algebra can often appear as a complex subject, but solving simple equations like 2x5-25 can be straightforward if you follow the steps carefully. In this guide, we will break down the process of solving this equation and explain each step in detail so that it can be easily understood.
Simplifying the Equation
Let's start with the equation 2x5-25
Step 1: Rearrange the Equation
The equation can be simplified to 2x35. Here, we observe that the term 2x5 can be simplified to 10, and then 10 - 2 equals 8, but since we have a 5 on the right side, we simplify it as follows:
2x5-25 can be rewritten as 2x35 (since 2x5-2 is the same as 10-28, but the equation simplifies to 2x35 for the next steps).
Step 2: Isolate the Variable
To isolate x in the equation 2x35, we need to move the 3 to the other side. This can be done by subtracting 3 from both sides of the equation:
2x35 Subtract 3 from both sides, 2x2
Step 3: Solve for x
Now that we have 2x2, we can divide both sides of the equation by 2 to solve for x: 2x/2 2/2 x 1
Therefore, the value of x is 1. You can verify this by substituting 1 back into the original equation:
2(1)5 - 2 5 10 - 2 5 5 5 (which is true)
Conceptual Understanding
Understanding the process and the rationale behind each step is crucial for solving similar algebraic equations. In this case, we simplified the original equation to 2x35, then moved the 3 to the right side, and finally divided both sides by 2. This method ensures that we reach the correct answer while reinforcing the fundamental principles of algebra.
Tips for Solving Algebra Equations
Here are a few tips to help you solve similar algebraic equations:
Always simplify the equation by combining like terms. Use inverse operations to isolate the variable. For example, if there is a subtraction, you should add the same value to both sides to balance the equation. Always double-check your answer by substituting it back into the original equation.Conclusion
Solving the equation 2x5-25 might seem daunting at first, but with a step-by-step approach, you can easily find the solution. By following the process above, you can solve similar algebraic equations with confidence.