Question

How do you solve `2| 3x - 2 | = 14`?

Answer 1

`x=3,-5/3`

Explanation:

Understand that:

`:.` Absolute values are always mean the distance from `0`

eg,`|-7|=7,|4|=4`

`color(blue)(2|3x-2|=14`

Divide both sides by `2`

`rarr(cancel2|3x-2|)/cancel2=14/2`

`rarr|3x-2|=7`

Now we can write that

`color(brown)(3x-2=7,3x-2=-7`

Solve for both the equations

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

`color(orange)(3x-2=7`

`rarr3x=7+2`

`rarr3x=9`

`color(green)(rArrx=9/3=3`

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

`color(indigo)(3x-2=-7`

`rarr3x=-7+2`

`rarr3x=-5`

`color(green)(rArrx=-5/3`

Answer 2

3 and #-5/3.

Explanation:

`|3x-2|=7` is the combined equation for the couple

`3x-2 = 7 and 2-3x=7`

The answer follows..