What's the difference between difficult and irresoluble?

Difficult

Definition:

(a.) Hard to do or to make; beset with difficulty; attended with labor, trouble, or pains; not easy; arduous.
(a.) Hard to manage or to please; not easily wrought upon; austere; stubborn; as, a difficult person.
(v. t.) To render difficult; to impede; to perplex.

Example Sentences:

(1) Virtually every developed country has some form of property tax, so the idea that valuing residential property is uniquely difficult, or that it would be widely evaded, is nonsense.
(2) Although solely nociresponsive neurons are clearly likely to fill a role in the processing and signalling of pain in the conscious central nervous system, the way in which such useful specificity could be conveyed by multireceptive neurons is difficult to appreciate.
(3) In practice, however, the necessary dosage is difficult to predict.
(4) Cor triatriatum (CT) is a rare congenital defect, surgically correctable, and sometimes difficult to diagnose by cardiac catheterization.
(5) By drawing from the pathophysiology, this article discusses a multidimensional approach to the treatment of these difficult patients.
(6) Past imaging techniques shown in the courtroom have made the conventional rules of evidence more difficult because of the different informational content and format required for presentation of these data.
(7) The way we are going to pay for that is by making the rules the same for people who go into care homes as for people who get care at their home, and by means-testing the winter fuel payment, which currently isn’t.” Hunt said the plan showed the Conservatives were capable of making difficult choices.
(8) In many cases, physicians seek to protect themselves from involvement with these difficult, highly anxious patients by making a referral to a psychiatrist.
(9) The diagnosis of variant- or Prizmetal-angina is difficult because if insufficient specificity of the tests.
(10) The detection of these antibodies is difficult owing to the lack of standardization and of specificity of the laboratory tests.
(11) It was so difficult to keep a straight face when I was filming a sauna scene with Roy Barraclough, who played the mayor of Blackpool.
(12) That is, he believes, to look at massively difficult, interlocking problems through too narrow a lens.
(13) Conversion of the active-site thiol to thiocyanate makes it more difficult to inactivate the enzyme by treatment with Cd2+.
(14) If they end up going to another club that is difficult to take.
(15) Cigarette consumption has also been greater in urban areas, but it is difficult to estimate how much of the excess it can account for.
(16) The most difficult thing I've dealt with at work is ... the terminal illness of a valued colleague.
(17) In that respect, it's difficult to see Allen's anthem as little more than same old same old, and it's probably why I ultimately feel she misses the mark.
(18) This hypothesis is difficult to substantiate with direct measurements using human subjects.
(19) Extrapolation of gestational age from early crown-rump lengths (CRLs) has been difficult because previously established tables of CRL versus gestational age have contained few measurements at less than seven to eight weeks from the first day of the last menses.
(20) Companies had made investments in certain energy sources, the president said, so change could be “uncomfortable and difficult”.