Which expression must be added to `3x-7` to equal 0?

Given:`" "3x-7`

Write as `color(green)(+3x-7)`

Everything must be turned into 0

`color(green)("Consider the "+3x)`

The `+3x` means that `3x` has been put with the expression and put with means add `->+`, so we need to remove it which is
subtract `-> -`

So for this part we have `color(white)(.)color(green)( 3x)color(red)(-3x)=0`
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`color(green)("Consider the "-7)`

Minus is remove so we have to put it back to make 0

So for this part we have `color(green)(-7)color(red)(+7)=0`
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`color(blue)("Putting it all together")`

`color(green)(3x-7 =?" "->" "3xcolor(red)(-3x)-7color(red)(+7)=0 )`

`" "color(green)(3x-7)color(red)(-3x+7)=0`

So you need to add the expression`color(red)(-3x+7)`

Numbers or terms which add together to give zero are called additive inverses. (adding opposites)

This means the same number, but one positive and one negative.

The following are all examples of additive inverses.

`(-5) + (+5) = 0`

`(+6b) + (-6b) = 0`

`(+x^2) + (-x^2) = 0`

This is a very useful concept which is used in solving equations, even if you were not aware of it.
(This is how one term is "moved to the other side")

The expression which must be added to `3x-7` to give 0,
is just its additive inverse.

`(+3x-7) + (-3x+7) =0`

(Same numbers, opposite signs)