SOLUTION: Use the form |x-b| < c or |x-b| > c to write an absolute value inequality that has the solution set 5 < x

SOLUTION: Use the form |x-b| < c or |x-b| > c to write an absolute value inequality that has the solution set 5 < x < 7.

Question 1201617: Use the form |x-b| < c or |x-b| > c to write an absolute value inequality that has the solution set 5 < x < 7.
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
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Inequality  5 < x < 7  is EQUIVALENT to (= is the same as; = has the same solution set as)

the inequality  |x-6 | < 1,  which is of the form you want.


As "b", you take the central point between the end-points 5 and 7:  b =  = 6.


As "c", you take the distance from mid-point "b" to any of the two end-points.

So,  c =  =  = 1.

Solved, with explanations.

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To see many other similar and different SOLVED problems on absolute value inequalities, look into the lesson
- Solving absolute value inequalities
in this site.

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