AUSTIN, Texas—Texas is poised to become the largest state in the U.S. to allow citizens to openly carry handguns, a change long sought by gun-rights activists.

The Texas House of Representatives on Friday voted 96-35 to allow residents with concealed-handgun licenses to openly carry their guns in public in holsters. A similar open-carry measure passed the Texas Senate last month; the two open-carry bills must be squared before being sent to Republican Gov. Greg Abbott, who has indicated support for the idea.

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