how to solve this inequality? What's the answer?

Question

The speed limit on the road is 30 miles per hour. Drivers on this road typically vary as much as 5 miles per hour. Represent this with an absolute value inequality.

Answer 1

"The speed limit on the road is 30 miles per hour. Drivers on this road typically vary as much as 5 miles per hour. Represent this with an absolute value inequality."

 

First, read and re-read the problem until you can put it into your own words.  How's this:

"The typical speed of drivers varies less than or equal to 5 miles per hour from the speed limit of 30 mph."

 

   Let x = typical speed of drivers

 so,

   absolute value of (speed x difference from 30) is less than or equal to 5

     |x - 30| <= 5

 

To remove the absolute value symbol, you must evaluate two inequalities:

   either

     (x-30) <= 5

    or

     -(x-30) <= 5     which also is (x-30) >= -5

         [when multiply by (-1) the sense of the inequality reverses]

 

     Combining those, we have:

       -5  <= (x-30) <= 5

     When we add 30, the sense of the inequality remains the same:

       25 <= x <= 35

Answer 2

The range to show is 5 miles slower than 30 (25) and 5 miles faster than 30 (35), so you need to show 25-35 miles. 

 

 

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