Solve for x |x-3|<7

Problem

|x−3|<7

Solution

1. Apply the definition of absolute value inequalities for the form |u|<a which translates to −a<u<a

−7<x−3<7

2. Isolate the variable x by adding 3 to all parts of the inequality.

−7+3<x−3+3<7+3

3. Simplify the arithmetic to find the range of values for x

−4<x<10

Final Answer

|x−3|<7⇒−4<x<10

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