We know that y varies directly as 6 more than three times x. When y is 2, then x is 1, and when y is 3, the value of x is k. What is the val

"y varies directly as 6 more than three times x"

  -- there is a multiplier in this formula, call this multiplier "m"

  -- then this equation becomes:  y  =  m·(6 + 3x)

 

"when y is 2, then x is 1"

  -- substituting these values into our formula, we have:  2  =  m·(6 + 3·1)

  -- solving for m:                                                               2  =  m·(9)

                                                                                         m  =  2/9

  -- therefore, our formula is:  y  =  (2/9)·(6 + 3x)

 

"when y is 3, the value of x is k"

  -- substituting these values into our formula, we have:  3  =  (2/9)·(6 + 3k)

  -- solving for k:                                                             27  =  12 + 6k

                                                                                       15  =  6k

                                                                                         k  =  5/2  or  2.5

 

Now, you need to find:  -|-2k + 3|

  -- substitute 2.5 into this expression to find the answer.