Brinson singled in the first, third and sixth innings, and doubled in the eighth.
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The 22-year-old outfielder was traded to the Brewers, along with right-handed pitcher Luis Ortiz (Brewers' No. 5) and a player to be named later, as Jonathan Lucroy and Jeremy Jeffress were dealt to the Rangers on Monday.
Brinson is hitting .246 this season, but may be heating up now that he's healthy -- he has nine hits in his past 14 at-bats. Brinson missed some time with a shoulder injury and upon his return, hit .268 in July, his best average in any month this year.
William Boor is a reporter for MLB.com. Follow him on Twitter at @wboor. This story was not subject to the approval of Major League Baseball or its clubs.