Question

How do you solve `abs(3x+2)=2`?

Answer 1

`color(red)(x = 0)` and `color(red)(x = -4/3)`.

We need to write two different equations without the absolute value symbols and solve for `x`.

These equations would be

(1): `(3x+2) = 2`
(2): `-(3x+2) = 2`

Solve Equation 1:

`3x+2 = 2`

Subtract `2` from each side.

`3x = 0`

Divide each side by `3`.

`x = 0`

Solve Equation 2.

`−(3x+2) = 2`

Remove parentheses.

`−3x−2= 2`

Add `2` to each side.

`-3x = 4`

Divide each side by `-3`.

`x = -4/3`

The solutions are `x = 0` and `x = -4/3`.

Check:

If `x = 0`,

`|3x+2|=2`
`|3×0 +2|= 2`
`|0 + 2| = 2`
`|2| =2`
`2=2`

If `x= -4/3`,

`|3x+2|=2`
`|3×(-4/3) + 2| = 2`
`|-4 + 2| = 2`
`|-2| = 2`
`2 = 2`