How do you solve $12/5 = x/6$ ?

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Answer 1 · 2016-02-20T14:48:59

This is the same approach as Simon L but in more detail

$x=14 2/5$

Objective: to end up with $x$ on one side of the equals sign and everything else on the other side.

$color(blue)("Principles behind Simons' short cut method")$

Simon used the shortcut method. This is based on: if you move something to the other side of the = you reverse 'what it is doing';

So if you had say: $" " x+3=2$ and you wished to move the $+3$

When you move the $+3$ to the other side it becomes $-3$

'~~~~~~~~~~~

Suppose you had $x-:3=2$ and you wished to move the $-:3$ to the others side.

So $x-:3=2" becomes " x=2xx3$

Another way of writing $x-:3" is " x/3$

so $x/3=2" becomes " x=2xx3$

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$color(blue)("The first principle method that the short cut method is based on")$

Given: $" " 12/5" "=" "x/6$

Write as: $color(brown)(" "12/5" "=" " x xx1/6)$

Multiply both sides by $" " color(blue)(6)$ giving:

$" "color(brown)(12/5 color(blue)(xx6)" "=" "x xx 1/6color(blue)(xx6)$

$" "color(brown)((12color(blue)(xx6))/5" "=" "x xx(color(blue)(6))/6)$

But $6/6=1$ giving:

$" "72/5" "=" "x$

$72 -: 5 = 14 2/5$ so we have

$" "color(red)(x= 14 2/5)$

How do you solve 12/5 = x/612/5 = x/6?