Question

Use deductive reasoning to show that the following procedure always produces a number that is equal to the original number.

Procedure: Pick a number. Multiply the number by 6 and add 8.

Divide the sum by 2, subtract twice the original number,

and subtract 4.

Answer 1

Pick a number $a.$

Multiply the number by 6 and add 8

$$6a+8$$

Divide the sum by 2

$$(6a+8)/2=3a+4$$

Subtract twice the original number, and subtract 4.

$$3a+4-2a-4=a$$

We see that if we pick arbitrary number $a$, then the following procedure always produces a number that is equal to the original number.

True.