Question

How do you solve `14 = t + 12`?

Answer 1

`t=2`

Explanation:

Given equation:`" "14=t+12`

`color(blue)("Preamble")`

Lets just think about this for a moment.

There is a link between the words 'equation' and the word 'equals'

Basically this is stating the 'intrinsic' value on the left is and must remain the same as the 'intrinsic value on the right.

Consider the example of `3=3` this is true

Suppose we subtracted 1 from just the left side then the statement would become: `3-1=3" "->" "2=3 larr color(red)("very false!")`

So to maintain the equals bit we have to do the same to both sides. Thus: `3-1=3-1`
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`color(blue)("Answering the question using first principles method")`

`14=t+12`

If we can change the 12 into 0 then `t+0=t` which is what we want.

Subtract 12 from both sides

`color(green)(14 color(red)(-12)=t+12color(red)(-12))`

`14-12=t+0`

`t=2`
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`color(blue)("Answering the question using first shortcut method")`

`14=t+12`

Move the 12 to the other side of the = and change its sign from + to -

`14-12=t`

`t=2`