Using Solve outputs for further calculations

Question

I am trying to solve a seemingly simple problem, namely the correct extraction of a single solution from Solve, to use in a subsequent calculation.

my function is a boring piecewise linear one;

y[x_] := Piecewise[{{0, 
x < 8642}, {((0.42 - 0.14)/(
   53666 - 8652)) x + (0.14 - ((0.42 - 0.14)/(53666 - 8652)
      8652)), 8652 < x <= 53666}, {0.42, x > 53666}}, x]

From here I solve to a particular value

sol = Solve[(x - y[x] x)/12 == 3000, x]

my answer becomes

{{x -> 62069.}}

Now, after having read around a bit, using Values and the first value of sol...( namely sol[[1]] ), I can calculate value for a subsequent equation;

Values[sol[[1]]] - ein 12 /. ein -> 1000
{50069.}

All is great.

However, now wanting to put sol into my original equation, I get the following;

0 {62069.} < 8642
{0.472269} 8652 < {62069.} <= 53666
0.42 {62069.} > 53666
{62069.} True

My assumption being, Values is providing a list to the function, and it can't solve it....and it gives me the answer back as if i had simply put in "y[a1]". How can I extract a value from Solve correctly to use in more automated subsequent calculations?

Thanks

Answer 1

Work with rule for the solution

sol = First@Solve[(x - y[x] x)/12 == 3000, x]

(*   {x -> 62069.}   *)

x - ein 12 /. sol /. ein -> 1000

(*   50069.   *)

(x - y[x] x)/12 == 3000 /. sol

(*   True   *)

y[x] /. sol

(*   0.42   *)