Which property of equality can be used to isolate a variable by adding the same value to both sides?

The property of equality that allows for isolating a variable by adding the same value to both sides is the Addition Property of Equality. This property states that if you have an equation ( a = b ), you can add a constant value ( c ) to both sides, resulting in ( a + c = b + c ). This maintains the balance of the equation and enables you to manipulate the equation in order to isolate the variable on one side.

For example, if you have the equation ( x + 3 = 7 ), you can apply the Addition Property of Equality by subtracting 3 from both sides, thereby isolating ( x ) and solving for its value. This fundamental concept is crucial in algebra, as it allows you to solve equations systematically and logically.