Question

How do you solve `3w - - 9= 81`?

Answer 1

`w=72/3`

Explanation:

`color(blue)("The teaching bit")`

Consider the number line as positive to the right and negative to the left.

The problem of this type of thing stems from a endemic habit that that has eventually become the accepted norm.

The consequence is that you can and may now read the mathematical sign of `'-'` as two things.

On the one hand it mat be read as declaring the CONDITION of negative state. The position on the number line

On the other hand it may be read as the ACTION of removing from the count of something. That is; minus, thus moving leftwards on the number line from your starting value.

`color(purple)(ul("This is the way I thing about it and very likely different to others"))`

As a first step automatically consider count as to the right. That is positive.

Now look at the sign in front of the number.

If the sign is 'minus' change direction of count.

Example: `-10`

Step 1. THINK ONLY of 10 to the right.

Step 2. Look at the sign. It is not positive but negative so change
`color(white)("dddddd")`direction towards the left.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

You have two 'subtracts' in front of the 9 so you `color(red)("change direction")` of count `color(red)("twice")`.

First: change from right to left.

Second: change from left to right.

In other words you have the equivalent of:

`3w+9=81`

Subtract 9 from both sides

`3w=72`

Divide both sides by 3

`w=72/3`