Question

Find a set of four integers such that their order and the order of their absolute values are opposite.

Answer 1

Four integers: -10, -8, -3,1.

Absolute values:
`\mid 1 \mid, \mid -3 \mid, \mid -8 \mid, \mid -10 \mid`

Explanation:

We have to find a set of four integers such that their order is opposite to the order of their absolute values.

Let the set of four integers arranged in increasing order be:

-10, -8, -3,1.

The absolute value is defined as:

• Absolute value describes the distance of a number on the number line from 0 to the number without considering which direction from zero the number lies.
• The absolute value of a number is never negative.
• We define the absolute value as:

`\mid a \mid = a, a>0\\~~~~~=-a, a<0`

The absolute value of the above number is:

10, 8, 3, 1

Increasing order of absolute values are:

1, 3, 8, 10 =
`\mid 1 \mid, \mid -3 \mid, \mid -8 \mid, \mid -10 \mid`