Question #cfc36

`\frac{x}{4}=\frac{3}{11}`

You can solve it by using proportion:

`x=\frac{4 xx 3}{11}=\frac{12}{11}`

`x=1\frac{1}{11}`

Have a look at https://socratic.org/help/symbols for formatting. Note the hash at the beginning and end of the typed text. This triggers the implementation of mathematical formatting.

Given: `x/4=3/11`

Our target is to have `x` on its own on one side of the equals and all the numbers on the other side

`color(red)("First principles method")`

If we can change the `1/4`bit from `x/4` into 1 then `x xx1->x` and we have solved it.

Write as

`color(green)(x xx1/4=3/11)`

Multiply both sides by `color(red)(4)`

`color(green)(x xx1/4color(red)(xx4)color(white)("ddd")=color(white)("ddd")3/11color(red)(xx4))`

`color(green)(color(white)("dd")x xx(color(red)(4))/4color(white)("dddd")=color(white)("ddd")(3color(red)(xx4))/11)`

`color(white)("dd")x xx1color(white)("ddddd") =color(white)("ddd")12/11`

`x=12/11`
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`color(red)("Shortcut method ")`

`color(brown)("Basically this is just remembering what happens with first principles")`

Consider the 4 from `x/4`

This is `x-:4` so move the 4 to the other side of the equals and use the opposite action to divide. Which is multiply.

So `x/4=3/11 color(white)("d")->color(white)("d")color(white)("d")x=3/11xx4`

`x=12/11`