Ramon Rosales Gomez appeals his sentence following his guilty plea to illegally reentering the United States after deportation and following a conviction for an aggravated felony. The district court sentenced Gomez to 41 months of imprisonment, a sentence at the bottom of the Sentencing Guidelines range. Although Gomez entered into a plea agreement wherein he waived his right to appeal his sentence, the Government has not relied on the waiver. Accordingly, we will not enforce it. See United States v. Story, 439 F.3d 226, 231 (5th Cir. 2006).

By raising arguments at the sentencing hearing that the district court clearly viewed as challenges to the unreasonableness of his sentence, Gomez arguably preserved his reasonableness challenge for appellate review. See United States v. Rodriguez, 523 F.3d 519, 526 n. 1 (5th Cir. 2008) (noting that the factual and legal arguments on appeal had been presented in the district court and concluding that the “ordinary standard of review” applied). We need not determine whether plain error review is appropriate, however, because Gomez’s arguments fail under either standard of review.

We “consider the substantive reasonableness of the sentence imposed under an abuse-of-discretion standard.” Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). “When the district court imposes a sentence within a properly calculated guidelines range and gives proper weight to the Guidelines and the 18 U.S.C. § 3553(a) factors, [this court] will give great deference to that sentence and will infer that the judge has considered all the factors for a fair sentence set forth in the Guidelines in light of the sentencing considerations set out in § 3553(a).” United States v. Campos-Maldonado, 531 F.3d 337, 338 (5th Cir. 2008) (internal quotation marks and citation omitted). “A discretionary sentence imposed within a properly calculated guidelines range is presumptively reasonable.” Id. “The presumption is rebutted only upon a showing that the sentence does not account for a factor that should receive significant weight, it gives significant weight to an irrelevant or improper factor, or it represents a clear error of judgment in balancing sentencing factors.” United States v. Cooks, 589 F.3d 173, 186 (5th Cir. 2009), cert. denied, - U.S. -, 130 S.Ct. 1930, 176 L.Ed.2d 397 (2010).

This court has rejected Gomez’s argument that application of U.S.S.G. § 2L1.2 renders a sentence unreasonable because it effectively results in the double counting of a defendant’s criminal history. See United States v. Duarte, 569 F.3d 528, *441 529-31 (5th Cir. 2009). Moreover, as noted by the district court, Gomez’s motive for returning does not outweigh his criminal history, in particular, the egregious nature of the prior burglary offense. Gomez thus has not shown that the district court made a clear error in balancing the sentencing factors set forth in § 3553, nor has he rebutted the presumption of reasonableness that attaches to his within-Guideline sentence. Accordingly, he has not shown error, plain or otherwise, in his sentence. See Cooks, 589 F.3d at 186.

AFFIRMED.