Question

Select the property of equality that is used to generate each set of equations.

Answer 1

I don't see the equations you want labeled. Send the sets of equations and I will pick the property for each one.

While you get those together, here is a short reference you can use to identify the property yourself:

Common properties of equality (what to look for)
- Addition property of equality
- If a = b then a + c = b + c.
- Look for the same number added to both sides.

- Subtraction property of equality
- If a = b then a − c = b − c.
- Look for the same number subtracted from both sides.

- Multiplication property of equality
- If a = b then a·c = b·c.
- Look for both sides multiplied by the same nonzero number.

- Division property of equality
- If a = b and c ≠ 0 then a/c = b/c.
- Look for both sides divided by the same nonzero number.

- Substitution property
- If a = b, then a can replace b in any expression (or vice versa).
- Look for one expression being replaced by an equal expression inside another equation.

- Transitive property
- If a = b and b = c, then a = c.
- Look for chaining equalities to deduce a new equality.

- Symmetric property
- If a = b then b = a.
- Look for simply swapping the two sides.

- Reflexive property
- a = a.
- Trivial equality used sometimes in proofs.

Other related properties (operation properties often used when manipulating equations)
- Distributive property: a(b + c) = ab + ac (used to expand or factor expressions).
- Identity/inverse: a + 0 = a, a·1 = a, a + (−a) = 0 (used when simplifying).

If you paste the specific equation sets, I'll label each one with the exact property used.