Question

At the Hendrix Design Company, the average starting salary for a new designer is $34,100, but the actual salary could differ from the average by as much $2,570. Which inequality could be used to determine if a salary, x, falls within this range?

A.
x - 34,100 < 2,570
B.
|x - 2,570| < 34,100
C.
|x - 34,100| > 2,570
D.
|x - 34,100| < 2,570

Answer 1

Let x be the salary. If x is more than the average, we want

`x-34100<2570`

If x is less than the average, we want

`34100-x<2570`

The two conditions can be summarized into

`|x-34100|<2570`

In fact, the absolute value of the difference of two numbers tells you "how far" those two numbers are, without taking into account which of the two is bigger.