Question

How do you solve `abs(3x+2)=14`?

Answer 1

`color(red)(x = 4)` and `color(red)(x = -16/3)`.

Explanation:

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

These equations would be

(1): `(3x+2) = 14`
(2): `-(3x+2) = 14`

Solve Equation 1:

`3x+2 = 14`

Subtract `2` from each side.

`3x = 12`

Divide each side by `3`.

`x = 4`

Solve Equation 2.

`−(3x+2) = 14`

Remove parentheses.

`−3x−2= 14`

Add `2` to each side.

`-3x = 16`

Divide each side by `-3`.

`x = -16/3`

The solutions are `x = 4` and `x = -16/3`.

Check:

If `x = 4`,

`|3x+2|=14`
`|3×4 +2|= 14`
`|12 + 2| = 14`
`|14| =14`
`14=14`

If `x= -16/3`,

`|3x+2|=14`
`|3×(-16/3) + 2| = 14`
`|-16 + 2| = 14`
`|-14| = 14`
`14 = 14`