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Absolute Value Inequality |x - 5| < 1










































Solving an Inequality

   • Solve the following absolute value inequality for x

      (Remember that an absolute value is always positive)

           |x - 5| < 1

   • Show all steps

Comments for Absolute Value Inequality |x - 5| < 1

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Sep 21, 2012
Solving an Inequality
by: Staff


Answer:

|x - 5| < 1

Math – graph of absolute value inequality


Since the inequality sign is “less than”, the values of x can be determined like this:

|x - 5| < 1

-1 < x - 5 < 1

Why ?

|x - 5| < 1 means that the value |x - 5| is a positive value which is less than 1 unit from a central point, regardless of the direction. In this case, the central point is the number 5.


-1 < x - 5 < 1

Add 5 to all three parts of the inequality

-1 + 5 < x - 5 + 5 < 1 + 5

-1 + 5 < x + 0 < 1 + 5

-1 + 5 < x < 1 + 5

-1 + 5 < x < 6

4 < x < 6




The final answer is:


Final Answer:


                 4 < x < 6




Thanks for writing.

Staff
www.solving-math-problems.com


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