Solving the Equation x 2x: A Step-by-Step Guide

Introduction

As you progress through AP Calculus, it#39;s inevitable that you will encounter various algebraic equations. One common equation that often trips up students is x 2x. However, this question is more of an exercise to test your understanding of basic algebra rather than an advanced calculus problem. This article will guide you through the steps to solve this equation and provide insights into the mathematical reasoning behind it.

Solving the Equation x 2x

The equation x 2x can be solved by following a few simple algebraic steps. Let#39;s break down the process:

Step-by-Step Solution

Step 1: Subtract x from both sides of the equation to collect like terms. Step 2: Simplify the resulting expression. Step 3: Isolate the variable x to find its value.

x  2x
x - 2x  0
-x  0
-1 * x  0
x  0

Alternative Method

Another way to solve the equation is by rearranging the terms:

Step 1: Subtract x from both sides of the equation. Step 2: Simplify the resulting expression.

x - x  2x - x
0  x

Explanation

The equation x 2x can be rewritten as 1x 2x. By subtracting x from both sides:

x - x  2x - x
0  x

This result shows that x 0 is the only solution to the equation. If you were to divide both sides by x, as in x / x 2x / x, you would get 1 2, which is a contradiction. This highlights the importance of being careful with algebraic manipulations, particularly when dividing by a variable, as it can lead to incorrect or nonsensical results.

Conclusion

In summary, the solution to the equation x 2x is x 0. This is a fundamental algebraic concept that, while trivial, is essential to understand for a solid foundation in more advanced mathematical studies, such as AP Calculus. By mastering these basic steps, you will be well-equipped to tackle more complex problems in calculus and other advanced mathematics courses.