Question

How do you solve `-4=-8+3(x-2)`?

Answer 1

`color(blue)(x=10/3`

Explanation:

`−4=−8+3(x−2)`

`−4=−8+3x− 3*2`

`−4=−8+3x− 6`

`−4=−8− 6 +3x`

`−4=−14 +3x`

`−4+14= 3x`

`10= 3x`

`color(blue)(x=10/3`

Answer 2

`x=10/3`

Explanation:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiplying the brackets:

`3(x-2)` is really 3 off `(x-2)`

That is `(x-2) + (x-2)+(x-2)`

So we end up with `x+x+x -2-2-2`

Which is 3 of `x` written as `3x` and we also have 3 lots of `-2` which is `-6`

So`3(x-2) =3x-6`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So the original equation of

`color(white)(xxxxxxx)color(brown)(-4=-8+3(x-2))`

Becomes

`color(white)(xxxxxxx)-4=-8 +3x-6`

`color(white)(xxxxxxx)-4=3x-14`

Add `color(blue)(14)` to both sides

`color(white)(xxxxxxx)color(brown)(-4) color(blue)(+14) color(brown)(=3x-14)color(blue)(+14)`

`color(white)(xxxxxxxxxxxxxx)10=3x`

Divide both sides by 3

`color(white)(xxxxxxxxxxxxxx)10/3 = 3/3 x`

`color(white)(xxxxxxxxxxxxxx)10/3 =x`

Write as per convention

`color(white)(xxxxxxxxxxxxxxxx)color(green)(x=10/3)`