inequality induction (1 Viewer)

[jxballistic]

Hi guys
For inequality induction during step 2, do we keep the inequality sign or do we swap to an equal sign? If you dont get what i mean look at the picture (inequality kept on right side, swaped to equal side on left side).

In every textbook I've seen, in every hsc solution, in another teacher's working at my school and in my tutors work, they switch to the equal sign.
But my teacher tells us to keep the inequality sign because what hes saying is if we change it back to an equal sign, we are saying that LHS (our first line) is EQUAL to that line which is not true. i.e my teacher means in the 3rd line on the left side we are "saying that 6k+3 = LHS" which is not true,that is why its wrong

I dont really care about which method is actually considered correct, as long as its accepted in the hsc. So which method is best to use for 3unit HSC ?(in...40ish days) My teacher said we'll lose marks if we change to an equal sign

 

[HeroicPandas]

u have a bad teacher

 

[Trebla]

A = B
> C
= D

The equality or inequality refers to the previous line by convention. In this case the statement means: A = B then B > C and C = D.

 

[braintic]

To add further to Trebla's explanation:
If on any line you include a LHS, the equality/inequality relates the new RHS to the new LHS.
If the line does not include a LHS, the equality/inequality relates the new RHS to the previous RHS.

 

[HSC2014]

Here's a more simplistic example:

Good:
2 = 4-2
> 3-2 (use of assumption here)
= 1

Bad:
2 = 4-2
> 3-2 (use of assumption here)
> 1

We stop using the inequality sign since otherwise it would say that some line is greater than the previous which is not true if we are only simplifying it etc. Hence it becomes clear only to use it where the assumption takes its roll.

 

[jxballistic]

I agree with what you guys say and i asked another teacher who checked some maths association or something and they do it the equal sign way. thanks guys