A machine packages rice into plastic bags. The weight of each bag of rice is supposed to be 8 ounces, but acceptable weights can vary by 0.1 ounces.

Which equation represents the minimum and maximum weights allowed for a bag of rice?

|x+8|=0.1
open vertical bar x plus 8 close vertical bar equals 0.1

|x−0.1|=8
open vertical bar x minus 0.1 close vertical bar equals 8

|x−8|=0.1
open vertical bar x minus 8 close vertical bar equals 0.1

|x+0.1|=8

Let [tex]y[/tex] denote a variable and let [tex]a[/tex] denote a constant. The equation [tex]|y| = a[/tex] means that the absolute value of [tex]y\![/tex] is equal to [tex]a[/tex]. Thus, both [tex]y = a[/tex] and [tex]y = (-a)[/tex] are solutions to the equation [tex]|y| = a\![/tex].

For example, if [tex]|y| = 0.1[/tex], then the valid values for [tex]y[/tex] would be [tex]y = 0.1[/tex] and [tex]y = (-0.1)[/tex].

In this question, the two valid values for [tex]x[/tex] are [tex]x = (8 + 0.1)[/tex] and [tex]x = (8 + (-0.1))[/tex]. Hence, if [tex]|y| = 0.1[/tex] such that either [tex]y = 0.1[/tex] or [tex]y = (-0.1)[/tex], then [tex]x = 8 + y[/tex] would mean that either [tex]x = (8 + 0.1)\![/tex] or [tex]x = (8 + (-0.1))[/tex].

Rearrange [tex]x = (8 + y)[/tex] to obtain [tex]y = (x - 8)[/tex]. Since [tex]|y| = 0.1[/tex], [tex]|x - 8| = 0.1[/tex].