91Ó°ÊÓ

Understanding how to isolate the variable in an equation is a fundamental skill in algebra. It involves doing the same operation on both sides of the equation to keep it balanced, while aiming to get the variable by itself on one side. In the exercise \( -2.28 = -3.8 n \) the variable \( n \) is first isolated by dividing both sides of the equation by -3.8. This is because the variable is initially multiplied by -3.8, and division is the opposite operation of multiplication.

Think of the equation like a balanced scale: whatever you do to one side, you must do to the other to maintain the balance. This process of isolating the variable leads us directly to the value of \( n \) without disturbing the equality of the equation.

Simplify by Performing the Operation

After dividing both sides of the equation by -3.8, the next step is to simplify the result to find the value of the variable. Simplification in this context means executing the division operation to get rid of the coefficient next to the variable. For our equation, simplifying \( \frac{-2.28}{-3.8} \) leads to \( n = 0.6 \) because a negative divided by a negative results in a positive number, and 2.28 divided by 3.8 equals 0.6.

Simplification makes equations easier to understand and solve. It may involve arithmetic operations like addition, subtraction, multiplication, and division, as well as combining like terms or applying properties of equality.

Check Your Work

To ensure that the solution for a variable is correct, it's necessary to verify it by substituting it back into the original equation. This step is crucial not only to confirm accuracy but also to develop good mathematical practice. Upon substituting \( n = 0.6 \) into \( -2.28 = -3.8 n \) and multiplying -3.8 by 0.6, we indeed find that both sides of the equation equal -2.28. This verifies that the solution \( n = 0.6 \) is correct. Solution verification serves as a proof that the steps we followed to isolate and simplify the variable were executed correctly, and it gives us confidence in our final answer.