91Ó°ÊÓ

Equation rearrangement is the process of manipulating an equation to get it in a desired form. In our given problem, we started with the equation \(2x - 3y = 6\), and we are tasked with solving for \(x\). The goal here is to transform the equation such that we isolate and solve for one particular variable.Sometimes, an equation might look complex, but by rearranging it, we can simplify our problem-solving process. To rearrange, consider the operations that maintain equality, such as adding, subtracting, multiplying, or dividing both sides by the same number.In this particular exercise, we rearranged the equation by adding \(3y\) to both sides. This step is crucial as it begins the process of isolating \(x\) on one side, leading us towards finding its solution.

Isolating variables is an important step when solving equations. It means getting one variable by itself on one side of the equation. For our problem, we focused on isolating \(x\) in the equation \(2x - 3y = 6\).Once we added \(3y\) to both sides, the equation became \(2x = 3y + 6\). Our next goal was to have \(x\) alone. With only \(2x\) on the left, the logical next step was to divide both sides by 2, giving us \(x = \frac{3y + 6}{2}\).Understanding how to isolate variables helps you solve equations so that you can find the value of unknowns. Isolating variables is all about strategic planning to simplify the equation.

Algebraic manipulation involves using mathematical operations to change the form of an equation or expression. It allows us to solve for specific variables or simplify equations for easy computation. In our problem, once we realized the equation was \(2x = 3y + 6\), algebraic manipulation skills were used to divide the entire equation by 2. It's essential to remember to perform the same operation on both sides of the equation to maintain equality.Another key point is always checking that the steps followed do not violate any arithmetic or algebraic rules. Proper manipulation ensures you arrive at the correct solution, which in this case is \(x = \frac{3y + 6}{2}\).