Question

How do you solve `-7w + 2 = -3`?

Answer 1

Just put 'w' on one side and numbers on the other.

Explanation:

So from the starting equation it goes like this:

-7w +2 = -3 /-2
-7w = -5 /:(-7)
w = `(5)/"7"`

Answer 2

`w=5/7`

`color(blue)("The tricks that show that the shortcuts actually work ")`

Explanation:

`color(blue)("Some thoughts!")`
`color(brown)("The other solution shows the shortcut methods which are both")` `color(brown)("very valid and speed everything up very much. This text explains")` `color(brown)("the foundations upon which those shortcuts are based.")`

The objective is to have a single w on one side of the = and everything else on the other side. This format (equation) declares the worth of a single 'w'.

The w is already on the left hand side (LHS) so we do not need to move it.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 1")`
There is a 2 on the left so we need to 'get rid of it'

Subtract `color(blue)(2)` from both sides giving:

`color(brown)((-7w+2)color(blue)(-2)=(-3 )color(blue)(-2))`

`-7w +2-2=-3-2`

But `color(white)(..) +2-2=0" and "-3-2=-5color(white)(..)` giving:

`-7w+0=-5`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 2")`

Make `-7w" into "+7w`

Multiply both sides by `-1` giving:

`7w=5`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 3")`

Isolate w
Divide both sides by 7 `(-: 7 " is the same as "color(blue)( xx1/7))`

`color(brown)(7wcolor(blue)(xx1/7)=5color(blue)(xx1/7))`

`7/7 w= 5/7`

But `7/7 =1` giving:

`w=5/7`