1. |3x-19|>5-x holds for all values of x.
we can open module:
x>19/3, so 3x - 19 > 5 - x and x > 6 (=18/3) - ok
x=19/3, so 0 > 5 - 19/3 or 0>-4/3 - ок
x<19/3, so - 3x + 19 > 5 - x and 14 > 2x or x < 7 (21/3) - ok
The whole expresion is true
2. There is no value of x for which |2x-10| <4-x holds.
the module is positive, 4 - х will be postivie only for x < 4. We can easaly test value x = 1,2,3 and forx<=0 the module can be opened as
...
we can open module:
x>19/3, so 3x - 19 > 5 - x and x > 6 (=18/3) - ok
x=19/3, so 0 > 5 - 19/3 or 0>-4/3 - ок
x<19/3, so - 3x + 19 > 5 - x and 14 > 2x or x < 7 (21/3) - ok
The whole expresion is true
2. There is no value of x for which |2x-10| <4-x holds.
the module is positive, 4 - х will be postivie only for x < 4. We can easaly test value x = 1,2,3 and forx<=0 the module can be opened as
...
