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Use deductive reasoning to show that the following procedure always produces the number 6. Procedure: Pick a number. Add 4 to the number and multiply the sum by 3. Subtract 6 and then decrease this difference by the triple of the original number.

Answer :

Answer:

procedure always produces 6

Step-by-step explanation:

Let 'n' be the unknown number

Add 4 to the number : n+4

multiply the sum by 3.

multiply the sum n+4 by 3

[tex]3(n+4) is 3n+12[/tex]

Now subtract 6, so we subtract 6 from 3n+12

[tex]3n+12-6=3n+6[/tex]

finally decrease the difference by the tripe of the original number

triple of original number is 3n

[tex]3n+6-3n= 6[/tex]

so the procedure always produces 6

abidemiokin

The final result of the deductive reasoning produced 6. Proved!

Let the unknown number selected be "x"

If 4 is added to the number, the result will be x + 4

If the resulting sum is multiplied by 3, the resulting expression will be 3(x+4)

  • Subtracting 6 from this expression will be 3(x+4) - 6

  • Triple of the original number is 3x

Taking the final difference between 3(x+4) - 6 and 3x will be 3(x+4) - 6 - 3x

On expansion:

[tex]= 3(x+4) - 6 - 3x\\=3x + 12 - 6 - 3x\\=3x-3x+12-6\\=0+6\\=6[/tex]

Hence the final result of the deductive reasoning produced 6. Proved!

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