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Solving equations is about finding the value of the variable that makes the equation true. When you have an equation like \( a - 6 = 9 \), the addition property of equality is very helpful. This property states that you can add the same number to both sides of an equation and it will still hold true.

To solve \( a - 6 = 9 \), you want \( a \) by itself on one side. That means you need to get rid of the \( -6 \) with \( a \). You can do this by adding 6 to both sides of the equation because when you add something to one side of the equation, you must do the same to the other side to keep it balanced. So, when you add 6 to both sides, the equation \( a - 6 + 6 = 9 + 6 \) simplifies down to \( a = 15 \). Now you have solved the equation, and you know that \( a \) is 15.

The isolation of a variable means getting the variable by itself on one side of the equation. This process is crucial because it allows you to clearly determine the value of the variable.

In the equation \( a - 6 = 9 \), the variable \( a \) is not isolated because it has \( -6 \) attached to it. To isolate \( a \), you need to remove \( -6 \). This involves adding 6 to both sides, thanks to the addition property of equality.

• The left side becomes \( a - 6 + 6 \), simplifying it to \( a \).
• The right side becomes \( 9 + 6 \), resulting in 15.

With \( a \) isolated, you directly see that \( a = 15 \). This makes it clear and simple to understand the solution.

Checking your solutions is an important step when solving equations. It confirms that your answer is correct and ensures no errors were made during calculations.

To check the solution for the equation \( a - 6 = 9 \) where \( a = 15 \), substitute 15 back into the original equation, replacing \( a \).

• Substitute to get \( 15 - 6 = 9 \).
• Simplifying this gives \( 9 = 9 \).

Since both sides are equal, the equation holds true, confirming that \( a = 15 \) is the correct solution. This verification step assures you that your math works accurately and provides peace of mind.