B737-700 CREW WAS UNABLE TO EXTEND THE TRAILING EDGE FLAPS PAST FLAPS 1.

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WHILE COMING IN TO LAND; WE WERE UNABLE TO ATTAIN TRAILING EDGE FLAP EXTENSION BEYOND 1 DEG. THE CHKLIST LED US TO THE ALTERNATE FLAP EXTENSION PROC; WHICH PROVED UNSUCCESSFUL (IN FACT; WHEN TOGGLING THE ALTERNATE EXTENSION SWITCH DOWN; THE TRAILING EDGE FLAPS WENT UP IN THE OPPOSITE DIRECTION). DISPATCH AND MAINT CTL WERE CONSULTED. ALL SAFE AND LOGICAL OPTIONS WERE EXPLORED; AND THE DECISION WAS MADE TO LAND ON RWY 19L WITH THE LEADING EDGE DEVICES OUT AND ONLY 1 DEG OF TRAILING EDGE FLAPS EXTENDED. AS A PRECAUTION; AN EMER WAS DECLARED. THE SUBSEQUENT APCH AND LNDG WERE UNEVENTFUL. THE PAX WERE BRIEFED BY MYSELF TWICE; AND THE MESSAGE EXPRESSED THAT THIS WAS NOT A DANGEROUS SIT. THE FLT ATTENDANTS WERE BOTH PREBRIEFED; AND POSTBRIEFED WITH NO SUBSEQUENT CONCERNS. WHILE DEPLANING; EVERYONE EXPRESSED GRATEFULNESS. THERE WERE NO NEGATIVE COMMENTS OR CONCERNS EXPRESSED BY THE PAX. MAINT WAS BRIEFED FACE-TO-FACE ALONG WITH A LOGBOOK WRITE-UP. THEY MENTIONED TO ME THAT THIS WAS A PREVIOUS WRITE-UP.