SOLUTION: "Describe how to use an absolute-value inequality to find all the values on a number line that are within 5 units of -6."

"The DISTANCE is the DISTANCE (in absolute value)"


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-15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4

Let x be a variable that can take on any value that is within 5 units of -6.

Then the DISTANCE from any value of x to -6 is the DIFFERENCE (in absolute
value.  The DIFFERENCE is x-(-6) and in absolute value is |x-(-6)| and we
can simplify that to |x+6| and to make that distance (difference) less that
5 units we write  

|x+6| < 5

You can also do it by starting with the inequality looking at the
number line above: 

-11 < x < -1 

Then add the opposite of -6, which is +6 to all three sides:

-11+6 < x+6 < -1+6

   -5 < x+6 < 5

       |x+6| < 5

Edwin