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The given inequality describes those and only those real numbers x that
2x is remoted from the number 8 on the number line not closer than 10 units.
Hence,
EITHER 2x >= 8 + 10 = 18, ----> x >= 18/2 = 9
OR 2x <= 8 - 10 = - 2, ----> x <= -2/2 = -1.
ANSWER. The solutions are x <= -1 or x >= 9.
Solved.
You may get THE SAME ANSWER by writing the given absolute value equation in the form
-10 <= 2x-8 <= 10
and solving this compound inequality.
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See the lesson
- Absolute Value equations
in this site.
