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(Part 9if of 11)
This message is best understood by first reading
“Algebra, Subtraction-Addition, Equality-Inequality: 4 of 5”
1. In the previous message, 7 + 5 does equal 12. We simply expanded the understandings to show what took place before, during and after so we can gain fuller understandings of the purpose of mathematics-arithmetic. Here are all the numbers and operators involved:
a) 7 + 5 = _____, the
initial equation, which we determined to be an inequality.
b) 7 = 1, the
pre-initial inequality that is not given using the Current Method of teaching math. The previous message provides the underlying context to recognize this inequality exists.
c) 7, the initial amount on the left side because it comes before the operator plus sign.
d) 5, the amount being added to the left side. 5 is the adjustment.
e) = shows we are trying to create equality or maintain equality.
f) -5, the amount being subtracted from the right side. Since +5 took place on the left side, that means 5 of something was being added to the left side, thus 5 must be also be adjusted from the right side because we started with an inequality. -5 is the adjustment. This amount was inferred because it is not given to us using the Current Method of teaching.
g) “x” is the unknown on the right side.
h) 12, the initial answer to “x”
i) 17, the initial amount on the right side. Determined by the Ancient Method of teaching math.
j) 24, the total amount of the whole, 7 = 17 initially as an inequality, then 12 = 12 after creating an equality.
k) 10, the difference between 7 on the left and 17 on the right. This difference was split into 5 and 5 by subtracting 5 from the right and adding 5 to the left. (This is why + 5 is shown. Unfortunately -5 is omitted in the Current Method).
l) RULE: The total difference in two sides of an inequality is two times the amount being added to or subtracted from one side. We add this total difference to the side the adjustment is being made to in order to the determine the pre-initial amount on the other side. OR We subtract the difference on the side being subtracted from. [which one is used depends on which one is known in the initial equation]
Applying The Rule:
7 + 5 = _____, means 5 is being added, thus the difference is 2 x 5=10.
We add 7 and 10 to get 17 on the right side
The pre-initial inequality is 7 = 17
We must know these things in order to solve the equation properly. In other words, we must know these things in order to manipulate resources to create the desired effect - to create equality or inequality.
2.
Double-Checking Using 7 = x + 3: Current New School Method:
a) 7 = x + 3
b) 7 - 3 = x + 3 – 3
c) 4 = x (final answer)
d) Now we substitute to double-check:
e) 7 = x + 3
f) 7 = 4 + 3
g) 7 = 7 (not considered part of the answer)
h) This method does not provide any understandings, just how to manipulate numbers.
3.
Double-Checking Using 7 = x + 3: Ancient Old School Method:
a) Continuous training in knowledge of self in relation to all else.
Includes but not limited to contextual knowledge of the whole, equations, equality, inequality, balance, imbalance, purpose of maintaining, cause and effect)
Presupposition: We live in a universe that is the whole. Everything taking place within this whole must balance itself out. Every action must and does have a corresponding opposite reaction. This is called a reciprocal relationship. Therefore, when you see a change in anything, try to understand what the corresponding change(s) are taking place. This will bring fullness of understanding due to understanding the whole nature of change. In terms of math equations, each equation must be formatted to reflect changes being made are taken into account on both sides.
Incorrect format: 7=x+3. Correct format: 7-3=x+3.
Incorrect answer: 4. Correct answer: 1. This is still not the complete answer solution.
b) Pre-analysis must be performed and continuing re-analysis:
We can see 3 is the adjustment on the right, therefore 2 x 3 = 6 is the difference between the two sides.
Since 3 is on the side being added to, and we don't know “x,” we subtract the difference from the left side.
7 – 6 = 1. This is the initial amount on the right side. (we already know the amount on the left side is 7)
The pre-initial inequality is 7 = 1. This is what exists before making the adjustment of +3
The whole total is 8 ( 7 + 1), which again shows us the difference of 6.
c) Determine type and amount of adjustment.
Since this is an inequality, the opposite adjustment must be made to both sides.
We already know the adjustment is shown as + 3 on the right side, thus must be -3 on the left side, if we want to create equality.
d) We can now see the steps that lead to the final equation:
7 = x + 3, initial equation (inequality) transforms into
7 = 1, pre-initial equation (inequality) transforms into
7 - x = 1 + x , final equation (equality) (notice how different this is from 7 = x + 3)
Intuitively we already know the answer must be 4 = 4, because that's the only way to divide 8 equally when there are only two sides. Therefore, once we determine the whole total during pre-analysis, all we have to do is divide it by two.
e) Solve the final equation:
7 - x = 1 + x
7 – x + x = 1 + x + x
7 = 1 + 2x
7 - 1 = 1 + 2x -1
6= 2x
3 = x (this is how you calculate the adjustment using the long way or for more complex problems)
f) Now make substitutions to verify the adjustment creates equality:
7 – x = 1 + x
7 – 3 = 1 + 3
4 = 4 (this is still an intermediate answer)
g) The lesson is not done until more answers come from additional understandings:
The whole total went from 7 = 1 to 4 = 4, both still 8
Notice how in the Current Method, the final equality is 7 = 7 for a total of 14, but in the Ancient Method, the final equality is 4 = 4 for a total of 8. This is explained in the next section.
Use the initial equation provided by the Current Method, to determine the pre-initial equation of the Ancient Method.
Then use the pre-initial equation, along with other information from pre-analysis, to form the final equation. Thus we have transformed the Current Method into the Ancient Method, mainly through analysis informed by the optimal theory of the African Utamawazo.
Using the Ancient Method we went from inequality as the solution, to inequality as the pre-existing condition to equality as the solution.
Using the Current Method we went from inequality as the solution to inequality in a different form as the solution.
As the Current Method shows, it is possible to equate something, and do so unequally, and conclude you did so equally and have the numbers to prove it.
The main point of math problems is not to just simply add, subtract, multiply and divide numbers. More importantly the point is to recognize the difference between what an equality is and what an inequality is and then understand how to manipulate transform them or maintain them. Doing all of this in relation to self in relation to all else. Additional understandings are listed throughout Parts 1-5 of this series.
4.
Slickery Trickery Method:
a) Another name for the Current Method.
b) Current Method overstates totals. In the example above, the total is overstated by 6
Using Current Method: final equality is 7 = 7, thus whole total is 14
No way of double-checking, what we end up with because what we start with is not considered.
We are told you start out with an equality where things are balanced on both sides, then you add 3 to one side and end up with an equality.
Using Ancient Method: final equality is 4 = 4 , thus whole total is 8 after equality created.
This is proven by double-checking against the pre-initial inequality of 7 = 1, thus the total is also 8 before equality created.
c) A series of mistakes when using the Current Method:
The context is suboptimal.
The upfront assumption that the equation presented is an equality is faulty – even though it returns an answer that makes the equation appear equal.
This is only possible by ignoring or hiding the whole total we started with. Then using the difference to falsely inflate both sides, thus also falsely inflate the whole total.
We are not alerted to the fact that the equation, as stated, is an inequality, therefore x + 3 does not equal 7. It can't. It can only equal 7 by virtue of the adjustment of +3. When and where did the adjustment of -3 take place? Furthermore, x cannot equal 7, because if it did, the equation would start out as 7=7 and end up as 4=10, none of which makes sense, especially when only a +3 is introduced.
You cannot put half of an adjustment in an equation to achieve equality.
No, and neither can you fix it by making the other half of the adjustment during solving the problem in order to maintain balance throughout the process and reach true equality. This is why analysis, as a daily part of life and existence, must be ongoing. And it is, we just make poor use of it.
Both parts of the adjustment must be reflected in the initial equation as shown by the Ancient Method.
In the Current Method, we are not taught that +3 means an adjustment is being made
We are not taught +3 is only half of the adjustment.
We think 4 is the answer that represents what x was initially
Instead, 4 represents what x is AFTER adding 3 to it. (therefore x is 1 initially as shown by the Ancient Method)
d) Reconciling the two methods:
The difference between the totals using two methods represents “the difference” of 6 we calculated in the Ancient Method.
In the Current Method, due to a series of logic error mistakes, we ended up falsely inflating the total from 8 to 14 by adding the difference of 6 to the total rather than splitting the difference and redistributing it.
Also, even more sinister, this error also transforms both sides as follows:
Left side: 7 plus the 3 that wasn't finally subtracted = 10 on the left side.
Right side: 7 minus the 3 that wasn't an initial part of “x”. This is not the same as the separate +3 shown as the adjustment. This gives us 4 on the right side.
Thus the final equation using the Current Method of logic is to create an inequality of 10 = 4 which is the same as the initial inequality of 7 = 1. Both show a difference of 6 between the two sides.
Using the Current Method, we are led to think the two sides are 7 = 7, but they are actually 10 = 4. The Ancient Method reveals the shenanigans. Ashe! Asante Sana.
The Current Method is the kind of math arithmetic that quantifies the national debt/deficit that keeps rising giving us a false impression of prosperity and why we think our quality of life has improved, because our income rises based on the numbers. All false. We can't know how
quality has changed without
qualitative understanding achieved via sufficient analysis of the before, during and after effects of change.
e) Adding to the whole total can only take place out of Preexistence Waters of Nun due to expansion. All other additions to other dimensions must be subtracted from somewhere else in this universe, usually from the closest dimensions to us.
f) To briefly summarize a few points I find interesting:
The Current Method of teaching us how to manipulate numbers inflates the whole total, inflates both sides, does not help you understand whether or not equality was actually achieved, instead numbers are used to tell you equality has been achieved or decreased.
Using the Current Method, understanding is lost and glossed – over.
When you don't do opposite things to both sides of an inequality and you misstate and inflate the total, the net effect is more inequality, of course.
The equation for equality (the process to achieve it) must be setup in the proper format in order to achieve equality. This must be checked and rechecked continuously, before, during and after the fact.
Current thinking and behavior among the masses has been calibrated to equate things unequally, and conclude it was done equally based on numbers and other information improperly arrived at and used.
The Current Method admits you must do the same thing to both sides of an equality. It fails to do so in the setup of the problem, thus false equality is achieved.
The Current Method also admits you must perform the opposite operation to remove a number or variable from one side of an equation. Then carry that same adjustment to the other side. Yet when the initial problem is not setup properly, the discrepancy between the two sides that existed, gets hidden.
The Current Method teaches that an “equation” means you're always dealing with an equality. Instead “equation” means you are equating two things, comparing them. An equation can also be an inequality.
What determines whether or not it is an equality is the preexisting difference, the adjustments being made and the difference after the adjustments.
The Ancient Method shows us the solution to a problem is always a multi-part solution. No problem can be solved without analysis. And no existing state of equality or inequality can be maintained without ongoing analysis that changes the form of the equality or inequality according to the current set of conditions.
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