91Ó°ÊÓ

In any linear equation, we often come across two types of entities: variables and constants. Understanding these terms is essential for solving equations effectively.
Variables are symbols, typically letters, used to represent unknown values. In our example equation, \(7y + 3 = 38\), the letter \(y\) is the variable. Our goal is to find the value of the variable that makes the equation true.
Constants, on the other hand, are fixed numbers that do not change. In the equation \(7y + 3 = 38\), both 3 and 38 are constants. They provide specific values that are used to relate and manipulate the variable.
Recognizing variables and constants is crucial because it allows us to apply algebraic operations properly, ensuring we can systematically solve for the unknown.

The process of isolating a variable is a critical step in solving any equation, especially linear equations. The main goal here is to rearrange the equation to have the variable on one side by itself.
In our given problem, \(7y + 3 = 38\), the variable \(y\) must be isolated. The first step is to remove the constant term from the left side of the equation. We do this by using subtraction, which is the inverse operation of addition.

• Start by subtracting 3 from both sides of the equation.

This operation changes the equation to \(7y = 35\). Now, the variable term \(7y\) is by itself on the left side. This simplifies the equation, making it easier to solve for \(y\).
Isolation is all about simplifying the equation, preparing it for the next step, which involves dealing with the coefficient of the variable.

A coefficient is a number that multiplies a variable. In the expression \(7y\), 7 is the coefficient. Solving for \(y\) involves handling the coefficient through division.
To isolate \(y\), we need to eliminate its coefficient. The equation \(7y = 35\) can be solved by dividing both sides by the coefficient of \(y\), which is 7. This is because division is the inverse operation of multiplication, allowing us to "undo" the multiplication by 7.

• Divide both sides by 7: \(y = \frac{35}{7}\).

Performing this division gives \(y = 5\).
This step is crucial because it provides the solution for the variable. Once the division is completed, the value of the variable is found, completing the solution process.