91Ó°ÊÓ

When we solve linear equations, a common goal is to get the variable by itself on one side of the equation. This process is known as isolating the variable. Let's look at the provided equation, \(14y + 7 = 91\). Our first step is to move the constant term (the number without the variable) to the other side of the equation.
To do this, we subtract 7 from both sides of the equation. This helps us keep the equation balanced because what we do to one side, we also do to the other. Subtracting 7 from both sides looks like this:

$$14y + 7 - 7 = 91 - 7$$

This simplifies to:

$$14y = 84$$

Now, we have isolated the term with the variable and can proceed to solve for y. Remember, isolating the variable helps in making the equation easier to solve.

The balance method is crucial when solving linear equations. Imagine an old-fashioned balance scale where the left side must equal the right side.

In the equation \(14y + 7 = 91\), the left side and right side are balanced. If we add or subtract anything from one side, we need to do the same to the other side to keep it balanced.

By subtracting 7 from both sides in the first step, we kept the balance:

$$14y + 7 - 7 = 91 - 7$$

Which simplifies down to:

$$14y = 84$$

The aim is to maintain equality as we transform the equation to isolate the variable. Next, we divide both sides by 14 to keep the balance and solve for y:

$$\frac{14y}{14} = \frac{84}{14}$$

This leads us to:

$$y = 6$$

Using the balance method ensures that the solution is accurate and the equation remains equal throughout the process.

Solving linear equations using basic algebra involves applying simple operations like addition, subtraction, multiplication, and division to isolate the variable. We always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

In our example, \(14y + 7 = 91\), we first tackled the addition by subtracting 7 from both sides:

$$14y = 84$$

Next, we dealt with multiplication. Since y is multiplied by 14, we divided both sides by 14 to isolate y:

$$y = \frac{84}{14}$$

This simplifies to:

$$y = 6$$

Remember these key points in basic algebra:

• Perform the same operation on both sides of the equation to keep it balanced.
• Use inverse operations to cancel out terms (e.g., subtraction cancels addition).
• Follow the order of operations to simplify correctly.

By understanding and applying these simple rules, you can solve any linear equation.