Question

Simplify without absolute value bars.

a. |w - 4| for w < 4

b. |w - 4| for w ≥ 4

Answer 1

See explanation

Explanation:

Use definition of the absolute value of the number x:

`|x|=\left\{\begin{array}{l}x,\ x\ge 0\\-x,\ x<0\end{array}\right.`

1. When
`w<4,` then
`w-4<0`

so using the definition,

`|w-4|=-(w-4)=4-w`

2. When
`w\ge 4,` then
`w-4\ge 0`

so using the definition,

`|w-4|=w-4`