Which statement represents the subtraction property of equality?

Which statement represents the subtraction property of equality?

• A. ac = bc
• B. If a = b, then a + c = b + c
• C. If a = b, then a - c = b - c
• D. y - y1 = m(x - x1)

Answer: (C)

Subtracting the same value from both sides keeps equality true. If two expressions are equal, removing the same amount from both sides preserves that equality: a = b implies a − c = b − c. For example, if a and b are both 7 and you subtract 2, you get 5 = 5. This shows why the statement about subtracting the same quantity from both sides is valid. This concept is the subtraction counterpart to adding the same value to both sides (which is the addition property) and to multiplying both sides by the same value (the multiplication property). The other option, a line-form equation, isn’t about preserving equality through subtraction.

Subtracting the same value from both sides keeps equality true. If two expressions are equal, removing the same amount from both sides preserves that equality: a = b implies a − c = b − c. For example, if a and b are both 7 and you subtract 2, you get 5 = 5. This shows why the statement about subtracting the same quantity from both sides is valid.

This concept is the subtraction counterpart to adding the same value to both sides (which is the addition property) and to multiplying both sides by the same value (the multiplication property). The other option, a line-form equation, isn’t about preserving equality through subtraction.