How to scale and shift voltage signal?
This can be done in a single stage.



Moreover, it can be done by inspection, using a trick, explained below.

Using the trick, the gain of Vin amounts to R1/R4 = 100/120 on the plus side.  The gain of the 5 V ref is R1/R5 or 100/50, so its input is v5 * 100/50 = 10v on the negative side.  The output equation is thus Vin*10/12 - 10v. 

The other thing to watch is the magnitude of the input signals.  With Vin at 24 V the op amp plus pin is about 5v due to the divider of R2,R3,R4.  So its ok.

The rest of the resistors are the trick.  R4 is offset by R6 on the other pin of the op amp.  R5 is offset on the other side of the op amp by R3.  And finally R1 is offset on the plus side by R2.  The sum of the gains on the plus side (R1/R2 + R1/R3 + R1/R4) minus the gains on the minus side (R1/R5 + R1/R6) is 1.00.  If the sum of the gains is 1.00 then the individual gains can be determined by inspection as R1/Rx.  That's the trick.

If one wants, R2 and R3 can be combined.

Input bias currents also cancel out in this arrangement.

A proof of this trick is left to the reader.  While it works and allows one to design the algebraic function in a single stage, the proof is complicated and the method a little misleading.