Notes on Solving Equations (Chapter 1: Sides of Equation)

Chapter 1: Sides of Equation

Introduction to Isolation of the Variable

• The primary goal in solving algebraic equations is to isolate the variable.

Step-by-Step Process of Solving for x

Step 1: Adding to Both Sides of the Equation

• To start the process, we need to manipulate the equation. Let's denote our equation as:

  $2x - 8 = 4$

• The first operation is to add 8 to both sides of the equation:

  • Left Side: $2x - 8 + 8 = 2x$

  • Right Side: $4 + 8 = 12$

• Therefore, after performing this step, the new equation is:

  $2x = 12$

Step 2: Dividing by the Coefficient

• Next, we need to eliminate the coefficient of 2 that is multiplying x. This is accomplished by dividing both sides of the equation by 2:

  • Left Side: $\frac{2x}{2} = x$

  • Right Side: $\frac{12}{2} = 6$

• Now the equation simplifies to:

  $x = 6$

Conclusion

• The solution to the equation is:

  $x = 6$

• This process demonstrates practical steps in isolating the variable and finding the solution in algebraic equations, specifically through the operations of addition and division.