Subtraction Property of Equality
The same thing can be subtracted from both sides of an equation
The subtraction property of equality is a fundamental concept in algebra that allows us to simplify and solve equations by subtracting the same value from both sides of the equation. This property states that if we have an equation with two terms on each side, we can subtract the same value from both sides of the equation without changing the validity of the equation.
For example, consider the equation x + 3 = 10. To solve for x, we can use the subtraction property of equality by subtracting 3 from both sides of the equation:
x + 3 – 3 = 10 – 3
This simplifies to:
x = 7
We can verify that our solution is correct by substituting x = 7 back into the original equation:
7 + 3 = 10
This is true, so our solution is valid.
In general, the subtraction property of equality tells us that if a = b, then we can subtract the same value c from both sides of the equation and obtain a – c = b – c. However, it’s important to note that this property only works for subtraction – we cannot add the same value to both sides of an equation and expect to maintain its validity.
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