Lesson 3:  The 'x' by its own
Case 1.

Let�s say we were given this statement
How can we get rid of the 3 so we keep only the x?

Well, if the number 3 is multiplying by x � we simply divide by 3 to get
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Because 3 divided by 3 is equal to 1 we get x alone.
Case 2.

Now let’s say we were given this statement
How can we get rid of the 5 so we keep only the x?

The x is being divided by 5. In this case we multiply also by 5.
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As 5 divided by 5 is equal to 1 both fives disappear.

The result is that we keep the x alone, as we wanted
Case 3.

Another example follows:
How can we get rid of the 7 so we keep only the x?

The x is being added 7 units so we make just the opposite: we subtract 7 units.
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Because 7 – 7 is equal to zero both sevens disappear.

The x alone again.
Case 4.

This next example might seem difficult but it is actually very simple
Well, ‘x’ is being multiplied by 7/3. We must take the necessary action to make the 7/3 disappear.

We ask ourselves: What is the opposite of 7/3?
Answer: Just invert the numbers. The answer is 3/7

Let’s do it
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Because 3/7 multiplied by 7/3 is equal to 1 we keep only the ‘x’.

What we just made is the same as dividing 7/3 by 7/3 which could also be done and is also equal to 1. Again we are using the opposite operation.
Case 5.

Last example:
How can we get rid of the -2 so we keep only the x?

The x is being subtracted 2 units so we make just the opposite: we add 2 units.
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Because -2 + 2 is equal to zero both 'twos' disappear.

The x is alone again.


What we did in all 4 cases was simply using the opposite operations using the same numbers that were near the x.
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