Question

Two numbers have an absolute value of 16. Which of the two numbers is greater than 12?

Answer 1

The absolute value of -16 is 16 and the absolute value of 16 is 16. So we know that 16 is greater than 12 but -16 is not.

Answer 2

16

Explanation:

Given : Two numbers which have an absolute value of 16

To find: Which of the two numbers is greater than 12

Solution:

Absolute Value Function :

We know that for any number x,

`\left | x \right |=x\,;\,,x\geq 0\\\left | x \right |= -x\,;\,,x< 0`

For numbers 16 and - 16:

As -16 < 0,
`\left | -16 \right |=-(-16)=16`

As 16 > 0 ,
`\left | 16 \right |=16`

`\left | 16 \right |=16\,,\,\left | -16 \right |=16`

Here,
`16> 12` and
`-16< 12`

So, out of numbers 16 and - 16 such that
`\left | 16 \right |=\left | -16 \right |=16` , 16 is greater than 12.