Question

How do you solve `|x - 4|< 2`?

Answer 1

Solution is set of values:

`2< x< 6`

Explanation:

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

`x−4<+-2`

Step 1: Set up the positive portion of the `+-` solution.

`x−4<2`

Add `4` both sides:

`x-4+4<2+4`

`x<6`

Step 2: Set up the negative portion of the `+-` solution. When solving the negative portion of an inequality, flip the direction of the inequality sign.

`x−4>−2`

Add `4` both sides:

`x-4+4 > -2 + 4`

`x > 2`

The solution to the inequality includes both the positive and negative versions of the absolute value.

`x<6` and `x>2`

Solution is set of values:

`2< x< 6`