Decoding the Mystery of Solving for X: Moving Beyond "Getting X by Itself

In algebra, one of the most important concepts is solving for an unknown variable, such as x. One common phrase that is often used to describe this process is "getting x by itself." However, this phrase can be misleading for students and does not accurately convey the true objective of solving for x.

The phrase "getting x by itself" implies that the goal is to isolate x on one side of the equation, with no other terms or variables present. While this may be the end result, it does not provide any insight into the actual steps that need to be taken in order to solve for x.

Instead of focusing on "getting x by itself," students should be taught to think about the objective of solving for x in a different way. The true objective is to have the coefficient of x equal to 1 on one side of the equation. This is because when the coefficient of x is 1, it means that we have found the numerical value of x.

For example, let's consider the equation 2x + 3 = 5x - 2. To solve for x, we need to perform mathematical operations on both sides of the equation in order to eliminate any terms that do not involve x. In this case, we would subtract 2x from both sides to get 3 = 3x - 2. Now, the coefficient of x is 1, and we can see that x = 1/3.

By shifting the emphasis from "getting x by itself" to having the coefficient of x equal to 1 on one side of the equation, students will be able to better understand the problem-solving process and the steps needed to solve for x. This approach will help students to focus on the objective of solving for x, rather than getting caught up in the phrase "getting x by itself."

In conclusion, the phrase "getting x by itself" is often used in algebra to describe the process of solving for an unknown variable like x. However, this phrase can be misleading for students and doesn't accurately convey the true objective of solving for x. Instead, students should be taught to focus on the objective of having the coefficient of x equal to 1 on one side of the equation as a problem solving objective. This will help students to better understand the problem-solving process and the steps needed to solve for x.