UNDOING OPERATIONS
SO, HOW DO WE UNDO OPERATIONS?
First we need to understand what all of the operations that we will be undoing are.
So, the operations are:
So, how do we undo Addition?
By subtracting. Whenever you see a + sign and you want to undo it, you subtract whatever is being added.
An example of this:
0 = x + 23
If we want to know what x is, we undo the addition.
So we subtract 23 from the equation.
-23 -23
And we get that x = -23
Some Examples For undoing addition
4. x + 100 = 101
-12 -12
x = 24
-12 -12
x = -5
-5 -5
x = 7
-100 -100
x = 1
So how do we undo Subtraction?
With addition! Whenever you see a - sign and you want to undo it, you add whatever is being subtracted.
An example of this:
x – 20 = 35
If we want to know what x is, we undo the subtraction.
So we add 20 from the equation.
+ 20 + 20
And we get that x = 55
SOME EXAMPLES FOR UNDOING SUBTRACTION
+24 +24
x = 51
+ 50 +50
x = 53
+ 47 +47
x = 49
+57 + 57
x = 157
SO WHAT ABOUT MULTIPLICATION?
We undo multiplication with division. However, sometimes multiplication can be hard to spot.
So an example is this:
If we have something like: 2x = 40
2x is the same as saying 2 * x, so if we want x by itself we divide by 2.
___ ___
2 2
After we divide by 2, we have that x = 20
SOME EXAMPLES FOR UNDOING MULTIPLICATION
___ __
30 30
x = 2
___ ___
400 400
x = 1
____ ___
200 200
x = 1
___ ___
11 11
x = 11
SO THEN HOW DO WE UNDO DIVISION?
Following the same logic, if undoing multiplication is using division, then undoing division must mean we multiply.
If we want to undo division, we need to multiply. The easiest number to multiply by is the denominator so we can get x by itself
5 * * 5
After we multiply the entire equation by 5 we get that x = 125
SOME EXAMPLES FOR UNDOING DIVISION
20 * * 20
x = 100
100 * * 100
x = 2000
30 * * 30
x = 600
40 * * 40
x = 320
2 * * 2
x = 400
SO WHAT ABOUT WHEN YOU HAVE MULTIPLE PROCEDURES GOING ON AT ONCE?
Wait SADMEP?
Yes, to solve for x, we want to work in reverse.
Now, we don’t always have to, but it’s usually the easiest way to solve.
Here’s our example from before:
So, following SADMEP, what we want to do first is undo the subtraction.
To do that, we need to:
And what we’ll get is:
Again, following SADMEP again, what we want to undo now is the division
To do that, we need to:
And finally, we are left with:
So that’s the secret?
That’s the secret.
When we are trying to solve for x, the easier way to work out the problem is to use SADMEP instead.
Now, you don’t have to use SADMEP every time
But when you don’t, things can get really complicated.
Here’s what I mean:
Not using SADMEP
So this time around, we’re not going to solve using SADMEP
Instead, we’re going to use PEMDAS.
So, following PEMDAS, what we want to do first is undo the multiplication.
To do that, we need to:
And what we’ll get is:
Again, following PEMDAS again, what we want to undo now is the subtraction.
To do that, we need to:
And finally, we are left with:
Or, in other words:
So that’s why we use SADMEP
Again, only if we’re trying to find x.
If we’re trying to simplify an equation or expression, we use PEMDAS.
It may seem a little confusing, but let’s try a few more to explain.
EXAMPLE 1:
Solve the following for x:
So, following SADMEP, what we want to do first is undo the subtraction.
To do that, we need to:
And what we’ll get is:
Again, following SADMEP again, what we want to undo now is the division
To do that, we need to:
And finally, we are left with:
EXAMPLE 2:
Solve the following for x:
So, following SADMEP, what we want to do first is undo the subtraction.
To do that, we need to:
And what we’ll get is:
Again, following SADMEP again, what we want to undo now is the multiplication.
To do that, we need to:
And finally, we are left with:
EXAMPLE 3:
Solve the following for x:
So, following SADMEP, what we want to do first is undo the addition.
To do that, we need to:
And what we’ll get is:
Again, following SADMEP again, what we want to undo now is the division
To do that, we need to:
And finally, we are left with:
EXAMPLE 4:
Solve the following for x:
So, following SADMEP, what we want to do first is undo the subtraction.
To do that, we need to:
And what we’ll get is:
Again, following SADMEP again, what we want to undo now is the division
To do that, we need to:
And finally, we are left with: