Question

In the following solution of 14t + 7 = 28, what is the reason for the third step?

1. 14t + 7 = 28 (Given)

2. 14t = 21 (Subtraction Property of Equality)

3. t = 3÷2 ( ? )

A) Substitution Property of Equality
B) Division Property of Equality
C) Multiplication Property of Equality
D) Transitive Property of Equality

Answer 1

\(\div=division\) so what answer choice goes with that?

Answer 2

In we're looking to try and solve for t, we need to get t on its own.

So, given that we have 14t = 21 from the second step, we need to remove the '14' from in front of the t in some way.

What so we do?? Well, what we can do is divide both sides by 14:

\[\frac{ 14 }{ 14 }t = \frac{ 21 }{ 14 }\]

14/14 = 1, so we've solved our problem. Remember, we need to DIVIDE BOTH SIDES of the equation by the same thing, otherwise we are changing the equation itself, rather than just rearranging it.

\[t = \frac{ 21 }{ 14 }\]

We can simplify the fraction on the right by dividing top and bottom by 7 (the largest common factor):
\[t = \frac{ 3 }{ 2 }\]

So, given what we've just done, which of the options do you think we're proving @CamPayne ?

Answer 3

well it can't seem to be anything else but option B

Answer 4

Yes, that's correct! :)