Question

Complete the formal algebraic proof:

Given:

Prove:

Statements Reasons
1. 1. Given
2.
2.
3.
3.
4.
4.

a. Division Property of Equality
b.
c. Multiplication Property of Equality
d.
e.
f. Symmetric Property of Equality

Answer 1

I don't have the "Given" statement or the "Prove" statement from your problem — could you paste those lines? With that I can fill in the four statements and the matching reasons.

While you paste it, here is a concrete example (common exercise) showing the form of a completed 4-line proof so you can see how to match the reasons you listed.

Example problem:
Given: 1/x = 1/y, x ≠ 0, y ≠ 0
Prove: x = y

Proof (statements — reasons)
1. 1/x = 1/y — Given
2. (1/x)(xy) = (1/y)(xy) — Multiplication Property of Equality (multiply both sides by xy)
3. y = x — Simplify both sides: (1/x)(xy) = y and (1/y)(xy) = x
4. x = y — Symmetric Property of Equality

Notes:
- That uses the Multiplication Property (your reason c) and the Symmetric Property (f).
- The Division Property of Equality (a) could be used in alternate approaches (e.g., dividing both sides by 1/x), but multiplying by xy is usually simplest for this particular statement.

Send the exact "Given" and "Prove" from your exercise and I'll fill in the four statements and label each reason (a–f) exactly as your worksheet expects.