Question

How do you solve `|(3x + 4 )/ 6| = |-4|`?

Answer 1

`"For"` `|(3x+4)/6|=|-4|`

`x=20/3,-28/3`

Explanation:

For absolute value you are going to solve for positive and negative.
Like this.

`|(3x+4)/6|=|-4|`

So we are solving

`|(3x+4)/6|=4` `color(red)"AND"` `|(3x+4)/6|=-4`

---

`color(red)(|(3x+4)/6|=4)`

Multiply both sides by six to remove denominator
`(3x+4)/cancel6=4*6`

`3x+4=24`

Subtract 4 from both sides
`3xcancel(+4)=24-4`
`3x=20`

Divide by 3 so that we have "x" alone
`(cancel3x)/cancel3=20/3`

`x=20/3`

Now, `color(red)(|(3x+4)/6|=-4)`

This is the same process so I'll go through it a little quicker.

`|(3x+4)/cancel6|=-4*6`

`3x+4=-24`

`3xcancel(+4)=-24-4`

`3x=-28`

`x=-28/3`