To determine which property of equality was used to solve the given equation, let's closely examine each step of the solution:
1. Original equation:
[tex]\[
x - 5 = -14
\][/tex]
2. Step 1: Adding 5 to both sides of the equation:
[tex]\[
x - 5 + 5 = -14 + 5
\][/tex]
Here, we are adding the same quantity (5) to both sides of the equation. This step is essential for isolating the variable [tex]\( x \)[/tex] on one side of the equation.
3. Step 2: Simplifying both sides:
[tex]\[
x = -9
\][/tex]
On the left side, [tex]\( -5 + 5 \)[/tex] simplifies to [tex]\( 0 \)[/tex], leaving [tex]\( x \)[/tex]. On the right side, [tex]\(-14 + 5\)[/tex] simplifies to [tex]\(-9\)[/tex].
The property used in step 2 is crucial to maintaining the equality of the equation while simplifying it. This property is known as the addition property of equality. The addition property of equality states that adding the same number to both sides of an equation does not change the equality of the equation.
By reviewing these steps, it is clear that the correct answer to the question is:
A. addition property of equality
