Respuesta :

Answer:

[tex]|x-6| \leq 7.5[/tex]          

Step-by-step 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.

[tex]|x| = x, ~x > 0\\~~~~=-x, ~x < 0[/tex]

  • [tex]|a-b|[/tex] 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:

[tex]|x-6| \leq 7.5[/tex]

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.

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