FLC IN ACR B757 ON DEPARTING LAS WERE APPARENTLY GIVEN TURN R INSTRUCTION BUT READ BACK TURN L AND NOT CAUGHT BY THE CTLR.

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DEP CITY LAS SEP/XA/98 XA10. BEAUTIFUL CLR DAY. CAPT'S LOG PDC READ; 'ACR X; ATC CLRNC MEAD 2 PGS J72 GUP THEN AS FILED; MAINTAIN 7000 FT; EXPECT 15000 FT 2 MINS AFTER DEP; DISREGARD DEP/SID; FLY RWY HDG VECTORS PGS.' AFTER TKOF; CLRED TO DEP FREQ. DEP SAID AT 5 DME TURN L 080 DEGS; CLB TO 15000 FT. FO READ BACK '5 DME L TURN 080 DEGS; CLB TO 15000 FT.' DEP WENT ON TALKING TO OTHER ACFT. AT 5 DME; I STARTED A CLBING L TURN. WHILE IN THE TURN; DEP SAID TO EXPEDITE THROUGH 13000 FT TO MAINTAIN 15000 FT. SHORTLY THEREAFTER; DEP ASKED IF WE TURNED L; TO WHICH FO REPLIED AFFIRMATIVE. DEP SAID 'YOU WERE SUPPOSED TO TURN R; TURN FURTHER L HDG 360 DEGS; LEVEL AT 8000 FT.' FO REPLIED 'WE UNDERSTOOD A L TURN; LEVEL 8000 FT TURNING L 360 DEGS.' DEP THEN SAID 'TURN FURTHER L 330 DEGS TFC SEPARATION LOST.' ATC THEN TOOK US N OF LAS ARPT; THEN OVER BLD VOR. UPON ARR DFW; I CALLED LAS DEP TRACON AND TALKED TO THE SHIFT SUPVR. HE SAID WE WERE GIVEN A 'R TURN;' BUT READ BACK 'L TURN' AND THE CTLR DIDN'T CATCH OUR READBACK. HE SAID IT WAS THEIR PROB AND WOULD TAKE CARE OF IT INTERNALLY. LISTENING TO CLRNCS WHEN CONCENTRATING ON SEVERAL THINGS SOMEHOW YOU DON'T CLRLY UNDERSTAND. IN OUR CASE; TAKING OFF RWY 25R; HVY WT; RISING TERRAIN TO W OF FIELD; TURN DELAYED TO 5 DME INSTEAD OF 4 DME; MAKING SURE ACFT KEEPS CLBING; RESETTING MCP; CLRING FOR TFC. EVEN ON VFR DAY; 2 MAN COCKPIT GETS BUSY. DEP CTL HAD A HVY WORKLOAD ISSUING INSTRUCTIONS ONE AFTER ANOTHER. ANOTHER PROB. AFTER FLYING INTO LAS SEVERAL TIMES. EVERY TIME WHEN WE DIDN'T FLY THE PUBLISHED SID MEAD DEP; WE WERE GIVEN A L TURN; SO A L TURN DIDN'T SOUND UNUSUAL TO ME. SOLUTION: LISTEN UP HARDER AND QUESTION ATC MORE. DURING DAYLIGHT OP; ATC HAVE ACFT FLY PUBLISHED DEPS.