In 2005, Sean Lewis pled guilty to being a felon in possession of a firearm, a violation of 18 U.S.C. § 922(g)(1). As part of the plea agreement, the Government agreed that “[t]he defendant, the defendant’s attorney, and the Government attorney may make whatever comment and evidentiary offer they deem appropriate at the time of the guilty plea, sentencing, or any other proceeding related to this case.” The district court accepted the plea agreement and “agree[d] to be bound by that agreement.” The court then sentenced Lewis to 120 months’ imprisonment, to run consecutively with a separate 30 month sentence imposed upon revocation of his supervised release arising from an earlier conviction.
In 2009, the Government filed a Fed. R.Crim.P. 35(b) motion to reduce Lewis’s sentence due to his “substantial assistance in the investigation and prosecution of other individuals who have committed criminal offenses.” The motion briefly discussed the assistance that Lewis had provided, including testifying for the State of Illinois in the first-degree murder trial of Marcus Northern. It also noted that Lewis had “indicated that his family has been threatened by associates of Mr. Northern due to [Lewis’s] testimony against him.” Based on these considerations, the Government recommended that Lewis’s sentence be reduced by 24 months, a 20 percent reduction. On November 10, 2009, a telephonic hearing was held on the Rule 35(b) motion. Lewis did not participate in the hearing, nor was he even aware that the motion had been filed. However, Lewis’s counsel participated in the hearing and did not object to Lewis’s absence. The Government urged the court to grant only the 20 percent reduction it had recommended because Lewis is “a rather notorious thug” whose offense was “extremely egregious.” Lewis’s counsel largely agreed that the Government had not “misrepresented any of the facts concerning Mr. Lewis.” Although counsel indicated that he had “not spoken to Mr. Lewis,” he ventured that “he would want [a] 50 percent [decrease] if he were here to speak .for himself.” The district court granted the 24-month reduction recommended by the Government.
Almost two months later, Lewis learned that the Rule 35(b) hearing had been held in his absence. Dissatisfied with the 24-month reduction and upset that he had not been notified of the hearing, Lewis filed a pro se motion complaining of “bad faith” on the part of the Government and requesting a new Rule 35(b) hearing in which he could participate. However, Lewis did not mention his plea agreement in this motion or specifically argue that the agreement granted him a right to participate in the Rule 35(b) hearing. The district court denied Lewis’s motion. Lewis now appeals, arguing that the Government *761breached the plea agreement by allowing the hearing to go forward in his absence and thereby depriving him of his contractual right to “make whatever comment and evidentiary offer [he] deem[s] appropriate at ... any ... proceeding related to [his] case.”
“This court is without jurisdiction to review Rule 35(b) sentences unless one of four criteria are met under 18 U.S.C. § 3742(a).” United States v. Williams, 590 F.3d 579, 580 (8th Cir.2009). These four criteria are: “(1) the sentence was imposed in violation of law, (2) the sentence was imposed using an incorrect application of the sentencing guidelines, (3) the sentence is greater than the applicable guidelines range, or (4) the sentence is imposed for an offense without a sentencing guideline and is plainly unreasonable.” Id. (citing 18 U.S.C. § 3742(a)(1)-(4)). Lewis claims that he was denied the right to participate in the hearing in violation of his plea agreement. “Allowing the government to breach a promise that induced a guilty plea violates due process.” United States v. Jensen, 423 F.3d 851, 854 (8th Cir.2005). Accordingly, because Lewis claims that his sentence was “imposed in violation of law,” his Rule 35(b) sentence is subject to review under § 3742(a)(1).
The Government asserts that review of Lewis’s claim nevertheless is foreclosed by the appeal waiver included in Lewis’s plea agreement, which provides that:
The Defendant hereby knowingly and expressly waives any and all rights to appeal Defendant’s conviction in this case, including a waiver of all motions, defenses and objections which Defendant could assert to the charges or to the Court’s entry of judgment against Defendant, and any and all issues inhering therein. ...
We agree with the Government that this appeal attacks “the Court’s entry of judgment against Defendant” and is within the scope of the appeal waiver. However, “[i]f the government breaches the plea agreement, ... the plea agreement is no longer enforceable as before against the defendant.” United States v. Lovelace, 565 F.3d 1080, 1085 (8th Cir.2009). Therefore, we conclude that the appeal waiver does not prevent us from reviewing Lewis’s claim that the plea agreement was breached.
However, because Lewis did not specifically raise his claim of breach in the district court, either through his attorney at the Rule 35(b) hearing or in his pro se motion, our review is only for plain error. See id. at 1086 (“[W]hen a defendant seeks to avoid an appellate waiver contained in a plea agreement by arguing, for the first time on appeal, that the government breached the plea agreement, this court will review the forfeited claim (and related claims) under the plain error test.”).1 To *762prevail under plain error review, Lewis must show “(1) an error, (2) that was ‘plain,’ [and] (3) ‘affects substantial rights,’ and [that] (4) ‘the error seriously affects the fairness, integrity or public reputation of judicial proceedings.’ ” United States v. Rush-Richardson, 574 F.3d 906, 910 (8th Cir.2009) (quoting Olano, 507 U.S. at 735-36, 113 S.Ct. 1770).
The plea agreement in this case provides that “[t]he defendant, the defendant’s attorney, and the Government attorney may make whatever comment and evidentiary offer they deem appropriate at the time of the guilty plea, sentencing, or any other proceeding related to this case.” Lewis asserts that the plain language of this clause granted him the right to participate in the Rule 35(b) hearing. The Government responds that it never intended to give Lewis such a right and that “[t]he parties’ intent in agreeing to [this clause] must have been that the absolute right to be heard would only be preserved where a right to be heard already existed.” Since a defendant has no independent right to participate in a Rule 35(b) hearing, see Williams, 590 F.3d at 580, the Government contends that there was no violation of the plea agreement.
The Government’s assertion that it never intended to give Lewis the right he asserts is unavailing unless its subjective intent is reflected in the plain language of the agreement. See United States v. Martinez-Noriega, 418 F.3d 809, 815 (8th Cir.2005) (“When a dispute arises over' the meaning of a plea agreement, the court must ‘discern the intent of the parties as expressed in the plain language of the agreement when viewed as a whole.’ ” (quoting United States v. Taylor, 258 F.3d 815, 819 (8th Cir.2001))). As an interpretation of the plea agreement’s language, the Government’s proffered reading is unpersuasive. Interpreting the clause in question to guarantee a right to participate only where such a right already exists by law would make the clause mere surplus-age. “Plea agreements are contractual in nature and should be interpreted according to general contractual principles,” Jensen, 423 F.3d at 854, and it is a familiar principle of contractual interpretation that “contracts must be interpreted to give effect to every provision,” Keymer v. Mgmt. Recruiters Int’l, Inc., 169 F.3d 501, 505 (8th Cir.1999).
We conclude that the plain language of the plea agreement guaranteed Lewis the right to participate in the Rule 35(b) hearing. By its terms, the plea agreement gives Lewis the right to make comments or present evidence at “any ... proceeding related to this case.” A Rule 35(b) hearing plainly is a “proceeding related to this case,” and the right to make comments or present evidence at a proceeding necessarily encompasses the right to participate in that proceeding. By allowing the Rule 35(b) hearing to go forward without giving Lewis the opportunity to participate, the Government and the district court violated the plea agreement by which both had agreed to be bound. Consequently, the sentence imposed following the hearing was arrived at through a violation of Lewis’s due process rights, see Jensen, 423 F.3d at 854, and imposed in violation of law, see 18 U.S.C. § 3742(a)(1).
Further, we conclude that this error was plain. As just discussed, the *763plain language of the plea agreement granted Lewis the right to participate in the Rule 35(b) hearing. The Government’s suggestion that the plea agreement only grants a right to participate where such a right already exists by law is at odds with the language of the agreement and renders the clause in question a nullity. Moreover, even if the Government’s proposed interpretation were plausible, it at most would show that the plea agreement is susceptible of two interpretations and therefore ambiguous. “Where a plea agreement is ambiguous, the ambiguities are construed against the government.” Jensen, 423 F.3d at 854. Thus, even if the language of the plea agreement did not foreclose the Government’s interpretation beyond all doubt, the district court was bound to construe the agreement against the Government as guaranteeing Lewis’s right to participate in the Rule 35(b) hearing. By going forward with the hearing in violation of this right, the court committed an error that is “clear” or “obvious.” See Olano, 507 U.S. at 734, 113 S.Ct. 1770.
Moreover, we hold that Lewis has met his burden of showing that this error affected his substantial rights. Lewis’s counsel at the Rule 35(b) hearing did not provide the district court with significant information that Lewis claims he could have provided had he participated. While the Government and Lewis’s counsel only mentioned one prosecution in which Lewis had cooperated, Lewis’s pro se motions suggest that he had cooperated in the investigation or sentencing of at least fifteen other individuals. Further, while the Government’s motion cited Lewis’s claim that his family had been threatened due to some of his testimony, the court noted that “I don’t have much to go on with regard to that,” indicating that the court was interested in the threats against Lewis’s family and desirous of further information concerning the incident. Neither the Government nor Lewis’s counsel was able to enlighten the court further on the matter, but Lewis claims he would have been able to provide the court with the information it sought regarding the threats against his family. Given the significance of this additional information as well as the district court’s demonstration of interest in the threats against Lewis’s family, we conclude that Lewis has shown “a reasonable probability that, but for [the error claimed], the result of the proceeding would have been different.” See United States v. Dominguez Benitez, 542 U.S. 74, 82, 124 S.Ct. 2333, 159 L.Ed.2d 157 (2004) (alteration in original) (quoting United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)).
Finally, the error “seriously affects the fairness, integrity or public reputation of judicial proceedings.” See Rush-Richardson, 574 F.3d at 910 (quoting Olano, 507 U.S. at 736, 113 S.Ct. 1770). Allowing the Government to breach a plea agreement, especially one by which the district court agreed to be bound, implicates “the honor of the government, public confidence in the fair administration of justice, and the effective administration of justice in a federal scheme of government.” See United States v. Thompson, 403 F.3d 1037, 1039 (8th Cir.2005) (quoting United States v. Harvey, 791 F.2d 294, 300 (4th Cir.1986)). Accordingly, we exercise our discretion to notice the forfeited error.
For the foregoing reasons, we hold that Lewis has carried his burden of showing that the denial of his contractual right to participate in the Rule 35(b) hearing constitutes plain error. Therefore, we vacate Lewis’s conviction and remand to the district court for a new Rule 35(b) hearing in which Lewis is allowed to participate.
. The Government contends that because Lewis did not object to the alleged breach of his plea agreement, either through his counsel or in his pro se motion, he has affirmatively waived any right to participate in the Rule 35(b) hearing. The Government cites United States v. Gunter, 631 F.2d 583, 589 (8th Cir.1980), as holding that counsel may waive a defendant's right to participate in a proceeding by failing to object to the defendant's absence. Gunter predates the Supreme Court’s decision in United States v. Olano, 507 U.S. 725, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993), which clarified the distinction between waiver and forfeiture. While forfeiture of a right arises from a “failure to make the timely assertion of [the] right” and limits appellate review to plain error, id. at 733, 113 S.Ct. 1770, waiver is the “intentional relinquishment or abandonment of a known right,” id., and a waived claim is unreviewable on appeal. Any suggestion in Gunter that counsel may waive, as opposed to forfeit, a defendant’s right to be present merely by failing to object to the defendant’s absence does not survive Olano. As neither Lewis nor *762his counsel, even mentioned that Lewis’s plea agreement may have granted him a right to participate in the Rule 35(b) hearing, the record does not support the proposition that Lewis or his counsel intentionally' relinquished or abandoned a known right. Thus, we reject the Government's waiver argument.