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.

Algebra ->  Absolute-value -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
.

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 = %285%2B7%29%2F2 = 6.


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

So,  c = %287-5%29%2F2 = 2%2F2 = 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.