Question

Prove: if ac=bc and c≠ 0, then a=b?

Answer 1

To prove that if ac=bc and c is not zero, then a equals b, you divide both sides of the equation by c. This simplifies to a=b, as c cancels out when it is nonzero.

Step-by-step explanation:

To prove that if ac=bc and c≠0, then a=b, we can divide both sides of the equation by c, assuming c is nonzero. This allows us to cancel out c from both sides of the equation because any number divided by itself is 1 (except for 0). The division property of equality states that if two quantities are equal and you divide them both by the same nonzero quantity, the results will still be equal.

The proof is as follows:

1. Given: ac = bc and c ≠ 0
2. Divide both sides by c: (ac)/c = (bc)/c
3. Simplify both sides: a = b

Therefore, if ac=bc and c≠0, it can be concluded that a=b.