Question

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

Answer 1

`| x - 8 | = 0.1`.

Explanation:

The minimum weight allowed is
`(8 - 0.1) = 7.9` ounces. The maximum weight allowed is
`(8 + 0.1) = 8.1`.

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

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

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

Rearrange
`x = (8 + y)` to obtain
`y = (x - 8)`. Since
`|y| = 0.1`,
`|x - 8| = 0.1`.