Officials who backed a tuition increase of between 9 percent and 12 percent at Nevada’s eight public higher education institutions described the move, approved Friday, as difficult but their best hope to avoid cuts to faculty positions and academic departments. The regents voted 8 to 5 in favor of the proposal. The hikes will take effect over the next three years and will cover a systemwide annual budgetary shortfall of $46.5 million. Representatives of the Nevada System of Higher Education,