SOLUTION: At George�s Graphics and More, the average starting salary for a new employee is $57,600, but the actual salary could differ from the average by as much $3590. Write an absolut

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Question 856299: At George�s Graphics and More, the average
starting salary for a new employee is
$57,600, but the actual salary could differ from
the average by as much $3590. Write an
absolute value inequality to describe this
situation. Solve it.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x the actual salary.
you get 2 equations.
57600 - x <= 3590
57600 - x >= -3590
this fits the definition of absolute value which says that:
|a| <= b if and only if a <= b and a >= -b
in this problem:
a = (57600 - x)
b = 3590
a <= b becomes (57600 - x) <= 3590
a >= -b becomes (57600 - x) >= -3590
the absolute value equation becomes:
|57600 - x| <= 3590

if you solve for this absolute value equation, you will find that:
(57600 - x) <= 3590 and (57600 - x) >= -3590.

if you solve for x in each of these equations, you will get:
x >= 54010 and x <= 61190

this equation can also be written as:
54010 <= x <= 61190.

x can be any value between 54010 and 61190.

you can graph this function as follows:

graph y = |57600 - x|
graph y = 3590

the values for the graph of y = |57600 - x| have to be underneath the graph of y = 3590.

the graph was difficult to show, but i figured it out and it is shown below.
the scale of the map is in thousands.
57600 would be shown as 57.6
3590 would be shown as 3.59
because of this scale change, the equations that are graphed are:
y = |57.6 - x|
y = 3.59
the value of y = |57.6-x| is smaller than y = 3.59 when x is greater than (57.6 - 3.59) and x is smaller than (57.6 + 3.59).

that makes x greater than or equal 54.01 and x smaller than or equal to 61.19 on the graph.

in real life this means that the value of |57600 - x| <= 3590 when x is greater than or equal to 54010 and smaller than or equal to 61190.
this is consistent with what was derived earlier.
the graph supports it.
the only difference is the change of scale in order to make the graph more legible.