91Ó°ÊÓ

To solve linear equations, one important step is isolating the variable. This means getting the variable alone on one side of the equation. In our example, the variable is \(x\). To start isolating \(x\), we need to move all terms containing \(x\) to one side.
In the provided problem, we subtract \(2x\) from both sides:
\[2x + 10 - 2x = 4x - 2x\]
This operation simplifies to:
\[10 = 2x\]
This step is crucial as it sets up the equation for simple division to solve for \(x\). By isolating the variable, we make it easier to find its value.

Simplifying equations involves combining like terms and performing basic arithmetic operations. Once you have isolated the variable term in one side, the next step is to simplify the equation.
After rearranging the given equation, we had:
\[10 = 2x\]
This is already a simplified form, where the term with the variable is isolated and there are no more like terms to combine.
Simplification makes the problem easier to solve in the next steps.

Basic algebra involves understanding and manipulating algebraic expressions and equations. Key skills include isolating variables, performing operations on both sides of equations, and simplifying expressions.
Let's see how basic algebra is used in our problem:
1. Rearranging the equation:
- We moved the \(2x\) term to the right by subtracting it from both sides.
- This gave us a simpler equation \(10 = 2x\).
2. Solving for the variable:
- We divided both sides of the equation by 2 to isolate \(x\). This resulted in \[x = 5\]
Understanding these fundamental algebraic steps helps solve a wide variety of linear equations and builds a strong foundation for more advanced math concepts.