Question

How do you solve `4x+ 8=-4`?

Answer 1

x=-3

Have a look at how the first principles method work. The shortcut is a shortened version of it!

Explanation:

Given:`" "4x+8=-4`

`color(blue)("Shortcut method")`

Move the 8 to the other side of the equals

`4x=-4-8`

Move the 4 from `4x` to the other side of the equals

`x=(-4-8)/4 = (-12)/4=-3`

'~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using first principles method")`

Subtract `color(blue)( 8)` from both sides

`color(brown)(4x+8color(blue)(-8)= -4color(blue)(-8))`

`4x+0=-12`

Divide both sides by 4. This is the same as `color(blue)(xx1/4)`

`color(brown)(4xcolor(blue)(xx1/4)=(-12)color(blue)(xx1/4))`

`color(brown)(4/(color(blue)(4)) xx x=(-12)/(color(blue)(4)))`

But `4/4 = 1" and "(-12)/4 = -3` giving

`color(magenta)(x=-3)`