91Ó°ÊÓ

When solving linear equations, one of the most crucial steps is to isolate the variable. In our given exercise, the variable is represented by the letter 'p'. Isolating the variable means getting it alone on one side of the equation. This helps us easily identify its value.

To start, we examine our equation: \( p - 3.6 = 1.7 \). Our aim is to have 'p' by itself on the left side. This can be achieved by eliminating the number that is attached to 'p'. In this case, '-3.6' is subtracted from 'p'.

Simplifying an equation makes it easier to work with and reach the solution. Every time we perform an operation, like adding or subtracting, we need to simplify to see a clearer picture of what we're solving.

Once we understand that we need to isolate 'p', we proceed by reversing the subtraction of 3.6. This means we will add 3.6 to both sides of the equation:

\( p - 3.6 + 3.6 = 1.7 + 3.6 \)
By doing this, the left side simplifies to just 'p'. Simplifying the right side, we add 1.7 and 3.6, resulting in:

\( p = 5.3 \).
Now, the equation is simplified, and we can easily see that p equals 5.3.

The addition property of equality is essential to remember when solving equations. It states that you can add the same number to both sides of an equation without changing its equality. This property is fundamental because it maintains the balance on both sides.

In our exercise, we applied this property when we added 3.6 to both sides of the equation to isolate 'p':

\( p - 3.6 + 3.6 = 1.7 + 3.6 \)
By using the addition property of equality, we ensured that the equation remained balanced while simplifying it.

Always remember that whatever operation you choose to apply to one side of the equation, you must do the same for the other side. This way, the equality holds, and you steadily progress toward finding the solution.