Question

How do you solve `\frac { 1} { 4} y = - 8`?

Answer 1

The final answer is `-32`.

Explanation:

First, you want to get rid of the fraction so you multiply both sides by 4.

On the left, you would get rid of the denominator and be left with `1y` which is the same thing as `y`.

Then, on the right, you would multiply `-8` and `4` which will equal `-32`.

Finally, in the end, it will be left as `y=-32`.

Answer 2

`y=-32`

`color(purple)("Another teach in!")`

Explanation:

There are two approaches to this.

The prime one could and is referred to as 'first principles'.

The second is called 'shortcut method'. This basically jumps steps used in first principles and speeds up the calculation process.

Both these methods (for this question) have the objective of just having a single `y` on one side of the = and everything else on the other. So we have to 'move things around' to achieve this objective.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Shortcut method - with full explanation")`
`color(purple)("The process without explanation is very fast")`

On the left hand side (LHS) we have a `1/4`. This is interpreted as `1-:4`

The division is an operation. 'Move' the 4 to the other side of the = and apply the revers operation to the 4.

On the left it is divide so on the right is multiply

So we have:

`color(green)(1/(color(red)(4))y=-8" "->" "1color(red)(-:4)xxy=-8)`

becomes`" "color(green)(1" "xxy=-8color(red)(xx4))`

but `1xxy=y` giving

`" "color(green)(y=-32)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("First principle method - with full explanation")`

If you wish to move something that is multiply or divide on the LHS of = to the right hand side (RHS) then you change it to 1.

Anything multiplied or divided by 1 does not change
`color(purple)("To maintain the truth of an equation what you do one side you do to the other")`

Given:`" "1/4y=-8 color(green)(" "->" " [1/4color(red)(xx1)] xxy = [-8color(red)(xx1)]`

`" "color(green)([1/4color(red)(xx4)] xxy = [-8color(red)(xx4)])`

`" "color(green)([1color(red)(xx)(color(red)(4))/4] xxy = [-8color(red)(xx4)])`

But `4/4=1`

`color(green)(" " [1color(red)(xx1)] xxy = [-8color(red)(xx4 )]`

`" "color(blue)(y=-32)`