A number is more than 9 units from 3

Question

i would like to know how to make an inequality 

Answer 1

You must account for both the number being more than 9 units smaller than 3 and being more than 9 units larger than 3.  To do that, you set the absolute value of the difference between the number and 3 greater than 9.

 

Let x be the number

 

|x - 3| > 9

 

Now solve for x.

 

Suppose x - 3 is positive.  Then

 

x - 3 > 9 ⇒ x > 12

 

Suppose x - 3 is negative.  Then |x - 3| = -(x - 3) = 3 - x

 

Then

 

3 - x > 9 ⇒ x < -6

 

These are the 2 possibilities.