5 ≤ 2x-3 <  3

There is no solution because the 5 on the left is NOT less than 
or equal to the 3 on the right.

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Maybe the 3 on the right was a typo and should have been a 7 
instead. Then it would have a solution:

We solve for x in the middle

  5 ≤ 2x-3 <  7   <-We add +3 to all three sides to get rid of the -3
 +3     +3 < +3
----------------
  8 ≤ 2x   < 10   <-We divide all three sides by 2 to get rid of the 2

8/2 ≤ 2x/2 < 10/2

  4 ≤  x   <  5

Sometimes that is abbreviated as [4,5),

The bracket [ on the left means there is a ≤
between the 4 and the understood x.
The parentheses ) on the right means there
is a < between the understood x and and the 5. 

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But the problem stated has NO SOLUTION.

Edwin