Question

Use absolute value notation to represent the following: all numbers x whose distance from 6 is no more than 7.5 units

Answer 1

`|x-6| \leq 7.5`

Explanation:

We have to use absolute value notation to express the given statement.

Absolute value function:

• It is a function that contains absolute value symbol.

`|x| = x, ~x > 0\\~~~~=-x, ~x < 0`

• 
  `|a-b|` is used to express the distance between two points a and b on a number line.

We want to write a absolute value function for all numbers x whose distance from 6 is no more than 7.5 units.

Thus, we can write:

`|x-6| \leq 7.5`

This can be interpreted as the absolute value of difference between x and 6(both in positive sense and negative sense) is less than equal to 7.5 that is not more than 7.5 units.