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- WELCOME TO A LESSON ON PROBLEM SOLVING. THE GOAL OF THIS VIDEO IS TO SOLVE A VARIETY OF PROBLEMS MATHEMATICALLY. NOW WHEN WE START PROBLEM SOLVING, THE FIRST STEP IS GOING TO BE TO READ THE QUESTION SEVERAL TIMES TO UNDERSTAND EXACTLY WHAT YOURE LOOKING FOR, THEN WE WILL ASSIGN NEW VARIABLES TO THE UNKNOWNS, THEN WE WANT TO SET UP AN EQUATION AND SOLVE. SO LETS GO AHEAD AND TAKE A LOOK AT THIS FIRST EXAMPLE. 6 FEWER THAN 4 x A NUMBER IS 78. FIND THE NUMBER. SO WE HAVE TO REPRESENT 6 FEWER THAN 4 x A NUMBER. WELL, LETS START WITH HOW WE WOULD REPRESENT THE NUMBER. LETS LET X = THE NUMBER WERE LOOKING FOR. NEXT, WE WANT 6 FEWER THAN 4 x THIS NUMBER X. WELL, LETS START WITH 4 x A NUMBER. WELL, THAT WOULD BE 4X, BUT WE WANT 6 FEWER THAN 4 x A NUMBER. SO 6 FEWER THAN 4X WOULD BE 4X - 6 AND IS MEANS EQUALS 78. SO HERES OUR EQUATION. AGAIN, 6 FEWER THAN 4 x SOME NUMBER X. SO NOW WE NEED TO SOLVE THIS EQUATION. SO THE FIRST STEP, BECAUSE THERES NO FRACTIONS, DECIMA