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Primary results: Stacey Abrams wins Georgia Democratic primary for governor -- live updates

Voters went to the polls for primary elections in Georgia, Arkansas and Kentucky and primary runoff elections in Texas. Here are the results:

Georgia

In the Democratic primary in Georgia's gubernatorial race, Stacey Abrams has won to become the state's first female nominee for governor from either major party.  If Abrams wins the general election in November, she'll become the first black female governor in the U.S.

The former state House minority leader, Abrams beat former state Rep. Stacey Evans in Tuesday's race. Both are Atlanta-area attorneys. The race was characterized by a battle over their legislative records on education. 

Abrams is a celebrated romance novelist who made economic mobility and affordable health care cornerstones of her campaign. She garnered major party endorsements from Hillary Clinton, congressman John Lewis and Sen. Bernie Sanders.

Abrams would succeed Republican Gov. Nathan Deal, who has held the office since 2011 and is term-limited.

On the Republican side, the candidates running for governor are using the same playbook as those running in the West Virginia and Indiana primaries, with candidates racing toward President Trump and trying to one-up each other by embracing his tone, policies and rhetoric. All five GOP candidates are drawing a hard line on immigration, as Mr. Trump did during his successful presidential campaign. 

AP points to this ad: "State Sen. Michael Williams, former state co-chair for Mr. Trump's campaign, ran an ad featuring a 'Deportation Bus' that he says will be used to send home people in the country illegally. The back of the bus warns of murderers, rapists, kidnappers, child molesters and other criminals on board and says, 'Follow me to Mexico.'" 

In a debate hosted by the Atlanta Journal-Constitution and Channel 2 Action News Sunday, the candidates also took a hard line on gun control. None of the Republican candidates said new gun control measures were needed, after the Texas high school shooting two days earlier. 

CBS News rates the race for Georgia's 6th Congressional District as a competitive House race. Karen Handel, who won the nationally-watched special election against Jon Ossoff in 2017, is running unopposed in Tuesday's primary, but four Democrats are competing for the right to face her in the fall. 

Kentucky

A high school math teacher has defeated the majority leader of the Kentucky House of Representatives in the GOP primary, following a wave of education protests at the Kentucky Capitol and elsewhere around the country.

Travis Brenda narrowly defeated state Rep. Jonathan Shell on Tuesday to win the nomination for state House District 71. Two years ago, Shell was credited with helping orchestrate the first GOP takeover of the state House in nearly 100 years. But voters turned on him for his role in writing a state law that changed Kentucky's pension system.

Brenda credited a groundswell of teacher support and says it sends a message that teachers and public workers won't be silent. Brenda will face Democrat Mary Renfro in November.

At least 15 other current and former teachers were on Tuesday's ballot.

A gay man in eastern Kentucky has lost his bid to challenge a Republican county clerk who went to jail three years ago for denying him and others marriage licenses.

David Ermold was seeking the Democratic nomination for county clerk in Rowan County, Kentucky. He had hoped to challenge religious conservative Kim Davis.

In 2015 Davis said that "God's authority" prevented her from issuing marriage licenses to same-sex couples in the aftermath of an historic U.S. Supreme Court decision.

Ermold lost to Elwood Caudill in a four-way Democratic primary on Tuesday, despite a campaign that raised more than $200,000 with donations from at least 48 states.

Caudill will face Davis in the November general election. No one challenged Davis for the Republican nomination.

Texas

A Hispanic female ex-sheriff has won the Democratic runoff to become the first openly gay and first Latina nominated for governor. While Lupe Valdez's victory Tuesday breaks barriers, the 70-year-old former Dallas County sheriff faces long odds of ousting Republican Gov. Greg Abbott this fall.

She defeated Andrew White, the son of a former governor who pitched himself as a moderate Democrat in deep-red Texas.

The runoff generated little enthusiasm among Democrats. Valdez has struggled to raise money and fumbled some questions on policy. Party activists have also attacked her for cooperating with federal immigration agents as sheriff.

Former NFL linebacker and civil rights attorney Colin Allred has won the Democratic nomination to try and unseat longtime Dallas Congressman Pete Sessions in November.

Allred won Tuesday's runoff over former Obama administration official Lillian Salerno, who served in the Department of Agriculture.

Allred, also an Obama administration veteran, beat Salerno handily during Texas' March 6 primary. But he was forced into a runoff election by failing to capture a majority of the votes cast in that seven-way race.

Representing some of Dallas' wealthiest enclaves, Sessions has been in Congress since 1997.

Hillary Clinton beat President Trump in Sessions' district in 2016, even though her party didn't field a congressional candidate.

That's attracted national attention to a Session-Allred race - though the incumbent has so far outraised his challenger.

A retired Navy Seal has pulled an upset to capture the Republican nomination for a Houston congressional seat being vacated by U.S. Rep. Ted Poe.

Dan Crenshaw beat one-term state Rep. Kevin Roberts during Tuesday's Republican primary runoff. Roberts conceded less than two hours after polls closed.

That was a mild surprise since Roberts topped Crenshaw by about six percentage points during Texas' March 6 primary. But he headed to a second round because neither candidate won a majority of the votes cast in a nine-candidate opening round of voting.

Crenshaw will face attorney Todd Litton, who won the five-way Democratic primary in March.

Poe is stepping down after six terms in Congress. His district encompasses many of Houston's suburban Republican strongholds and is expected to stay safely Republican after November's general election.

Arkansas

Arkansas' governor says his victory in the Republican primary over a challenger who accused him of not being a true conservative means voters rejected "negative voices."

Hutchinson defeated a gun range owner, Jan Morgan, in Tuesday's primary. Hutchinson had dwarfed Morgan in fundraising and had touted $150 million in tax cuts he had signed into law since taking office. Morgan had criticized Hutchinson as not conservative enough on several issues, including tax cuts and health care.

Hutchinson's win came a day after Mr. Trump endorsed him in the primary. Hutchinson said he believed he was trending toward a win, but the president's endorsement gave him some last-minute momentum in the race.