Question

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

Answer 1

Here are common properties of equality, each stated briefly and shown with an example starting from 5y = 25.

- Addition property: If a = b, then a + c = b + c.
Example: add 3 to both sides → 5y + 3 = 25 + 3, so 5y + 3 = 28.

- Subtraction property: If a = b, then a − c = b − c.
Example: subtract 2 from both sides → 5y − 2 = 25 − 2, so 5y − 2 = 23.

- Multiplication property: If a = b, then a·c = b·c.
Example: multiply both sides by 2 → 10y = 50.

- Division property: If a = b and c ≠ 0, then a/c = b/c.
Example: divide both sides by 5 → y = 5.

- Substitution property: If a = b, you may replace a with b in any expression.
Example: since y = 5 (from above), substitute into 3y + 1 → 3(5) + 1 = 16.

- Symmetric property: If a = b, then b = a.
Example: from 5y = 25 we also have 25 = 5y.

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

- Reflexive property: Any quantity equals itself.
Example: 5y = 5y.

All of these operations keep the equality true as long as you apply the same operation to both sides (and avoid forbidden operations, e.g., dividing by 0).