Question

How do you solve `3x + 19 = 3 - 5x`?

Answer 1

`x=-2`

Explanation:

`3x+19=3-5x`

`:.3x+5x=3-19`

`:.8x=-16`

`:.x=-16/8`

`:.x=-2`

~~~~~~~~~

check:-

substitute `x=-2`

`:.3(-2)+19=3-5(-2)`

`:.-6+19=3+10`

`:.13=13`

Answer 2

`x=-2`

Explanation:

Given: `3x+19=3-5x`

To end up with all the `x` terms on the left sides add `color(red)(5x)` to both sides.

`color(green)(3x+19 = 3-5x color(white)("dddd") ->color(white)("dddd")ubrace(3xcolor(red)(+5x))color(white)("d") +19 = 3color(white)("d") ubrace(-5x color(red)(+5x)) )`
`color(white)("ddddddddddddddddddddddddd.d") darrcolor(white)("dddddddddddddd") darr`
`color(green)(color(white)("dddddddddddddddddd") ->color(white)("dddddd") 8xcolor(white)("ddd") +19 =3color(white)("...") +0)`

Subtract 19 from both sides `->color(white)("ddd") 8x =-16`

Divide both sides by `color(red)(8)`

`color(green)(8x=-16 color(white)("dddddddddd") ->color(white)("ddddd") 8/color(red)(8) x=-16/color(red)(8))`

But `8/8=1 and 1xx x = x`

`color(green)(color(white)("ddddddddddddddddddd") ->color(white)("dddddd") x=-2)`