Question

Which of the following is true? |−6| < 5 |−6| < |5| |−5| < |−6| |−5| < −6

the answer

Answer 1

The third one: `|-5| < |-6|`.

Explanation:

`|x|` represents the positive or the magnitude of the term inside the modulus symbol.

If you simplify the inequalities you will get some thing like this:

(1.)
`|-6| < 5`
`color(red)(6 < 5)`

This is a `color(red)("false statement.")`

(2.)
`|-6| < |5|`
`color(red)(6 < 5)`

This is a `color(red)("false statement.")`

(3.)
`|-5| < |-6|`
`color(blue)(5 < 6)`

This is a `color(blue)("true statement.")`

(4.)
`|-5| < -6`
`color(red)(5 < -6)`

This is a `color(red)("false statement.")`

Therefore, the third inequality is true.