Question

Absolute value equation |x+4|=2​

Answer 1

Answer and Step-by-step explanation:

`Hello!~`

`Let's~answer~your~question!`

`For~this~equation,We~know~either:~x+4=2~or~x+4=-2`

`There~are~2~possibilities~for~this~equation.`

Possibility - 1 :

`x+4=2`

`x+4-4=2-4~~~~~ (Subtract~4~from~both~sides)`

`x=-2`

Possibility - 2 :

`x+4=-2`

`x+4-4=-2-4`

`x=-6`

Answer:

`x=-2 ~or ~x=-6`

Answer 2

Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.

x−4=±2

Set up the positive portion of the ± solution.

x−4=2

Move all terms not containing x to the right side of the equation.

Tap for more steps...

x=6

Set up the negative portion of the ± solution.

x−4=−2

Move all terms not containing x to the right side of the equation.

Tap for more steps...

x=2

The solution to the equation includes both the positive and negative portions of the solution.

x=6,2