Question

If 5y = 25, which property of equality was used to keep the equation 5y – 7 = 25 – 7 equal?



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What other properties of equality could you apply to keep the equation 5y = 25 equal? Give an example of each.

Answer 1

The step 5y − 7 = 25 − 7 used the Subtraction Property of Equality (a special case of the Addition Property of Equality): if a = b then a − c = b − c (equivalently a + c = b + c). Subtracting the same number from both sides keeps the equation true.

Other properties you can apply to 5y = 25 (with an example for each):

- Addition Property of Equality: add the same number to both sides.
Example: 5y + 2 = 25 + 2 → 5y + 2 = 27.

- Multiplication Property of Equality: multiply both sides by the same number.
Example: 3·(5y) = 3·25 → 15y = 75.

- Division Property of Equality: divide both sides by the same (nonzero) number.
Example: (5y)/5 = 25/5 → y = 5.

- Symmetric Property of Equality: you may swap the sides.
Example: 25 = 5y.

- Transitive Property of Equality: if a = b and b = c then a = c.
Example: If 5y = 25 and 25 = 5·5, then 5y = 5·5.

- Substitution Property of Equality: you may replace one side with the other in an expression.
Example: In 3(5y) you can substitute 25 for 5y to get 3(25) = 75.

Each of these preserves equality because the same valid operation or replacement is applied to both equal quantities.