What should a be for the system of inequalities to have one solution? ( 1 )

rose2904ks 2022-06-11 Answered
What should a be for the system of inequalities to have one solution?
( 1 ) 3 x a 1 ( 2 ) | x 2 a 2 | 1
For them to have one solution, the solution must be an endpoint of an interval. (1) gives me
x a + 3
but I don't know how to proceed from here. Any hint would be appreciated.
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Answers (1)

popman14ee
Answered 2022-06-12 Author has 19 answers
The first it's
3 x a 1 0
or
3 + a x x a 0
or
a < x 3 + a .
The second it's
2 a + 1 x 3 + 2 a .
Now, we see that an unique possibility it's
3 + a = 2 a + 1.
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