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1) найти корни выражений под модулем:
это х=16 и х=4
2) на каждом из трех получившихся промежутков раскрыть модули по определению:
для x < 4: |x-4| = 4-x
|x-16| = 16-x
получим уравнение: 16-х - (4-x) = 2x
16-x-4+x = 2x ---> x = 6 (6>4) на этом промежутке нет корней...
для 4 ≤ x < 16: |x-4| = x-4
|x-16| = 16-x
получим уравнение: 16-х - x+4 = 2x
20 = 4x ---> x = 5 (5>4) это корень.
для x ≥ 16: |x-4| = x-4
|x-16| = x-16
получим уравнение: х-16 - x+4 = 2x
-12 = 2x ---> x = -6 (-6<16) на этом промежутке нет корней...
ответ: х=5
и всегда можно проверить: |5-16| - |5-4| = |-11| - |1| = 11-1 = 10 (=2*5)
|6-16| - |6-4| = |-10| - |2| = 10-2 = 8 (≠2*6)
