Question

How do you solve `4/5=x/9`?

Answer 1

`x=36/5`

Explanation:

Given:`" "color(brown)(4/5=x/9)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(magenta)("Using first principles")`

Multiply both sides by `color( blue)(9)`

`color(brown)(4/5color(blue)(xx9)=x/9color(blue)(xx9))`

`color(white)(.)`

`color(brown)((4color(blue)(xx9))/5=x xx(color(blue)(9))/9)`

But `9/9=1`

`36/5=x xx 1`

But `x xx1 = x`

`x=36/5`
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`color(magenta)("Using shortcut method")`

`4/5=x/9`

Take the 9 on the right over to the left and do the opposite of its action. Note that `x/9` is the same as `x-:9`

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

`4/5xx9=x`

`x=36/5`