So, you were labelled as an intending immigrant who entered without an immigrant visa. You filed for adjustment, they told you to leave but you didn't then you got picked up by ICE and placed in removal proceedings. INA 212(a)(7)(A)(i)(I) was the reason for the I-485 denial. A discretionary waiver is available for that but you didn't get it. Did they explain why not?
How did you orginally enter, for how long were you allowed to stay, what happened, and on what basis did you file for adjustment?
What else is listed on the NTA? You must be leaving something out, if you don't provide full information, you will will not get good advice.
It appears that you have now accumulated "unlawful presence" after being told to depart and have invoked at least a 3 year bar to re-entry. Once unlawful presence reaches 1 years, the bar grows to 10 years. A waiver (I-212) is available for that but you apply according to the instructions specific to your situation found at:
http://www.uscis.gov/portal/site/us...nnel=db029c7755cb9010VgnVCM10000045f3d6a1RCRD (depending on circumstances, you file with: DOS, CBP, EOIR, or USCIS)
INA 212=8 USC 1182
Sec. 1182. Inadmissible aliens
(a) Classes of aliens ineligible for visas or admission
Except as otherwise provided in this chapter, aliens who are
inadmissible under the following paragraphs are ineligible to receive
visas and ineligible to be admitted to the United States:
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(7) Documentation requirements
(A) Immigrants
(i) In general
Except as otherwise specifically provided in this
chapter, any immigrant at the time of application for
admission--
(I) who is not in possession of a valid unexpired
immigrant visa, reentry permit, border crossing
identification card, or other valid entry document
required by this chapter, and a valid unexpired
passport, or other suitable travel document, or document
of identity and nationality if such document is required
under the regulations issued by the Attorney General
under section 1181(a) of this title, or
(II) whose visa has been issued without compliance
with the provisions of section 1153 of this title, is inadmissible.
(ii) Waiver authorized
For provision authorizing waiver of clause (i), see
subsection (k) of this section.
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(k) Attorney General's discretion to admit otherwise inadmissible aliens
who possess immigrant visas
Any alien, inadmissible from the United States under paragraph
(5)(A) or (7)(A)(i) of subsection (a) of this section, who is in
possession of an immigrant visa may, if otherwise admissible, be
admitted in the discretion of the Attorney General if the Attorney
General is satisfied that inadmissibility was not known to, and could
not have been ascertained by the exercise of reasonable diligence by,
the immigrant before the time of departure of the vessel or aircraft
from the last port outside the United States and outside foreign
contiguous territory or, in the case of an immigrant coming from foreign
contiguous territory, before the time of the immigrant's application for
admission.
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