If 9 is added to twice a number and this sum is multiplied by 6, the result is the same as if the number is multiplied by 7 and 14 is added to the product. what is the number?

Let 'the number' be A.

9 is added to twice a number... so...

9 + 2A

this ^ sum is multiplied by 6

6(9+2A)

This ^ is equal to to the number times by 7 plus 14... so...

6(9+2A) = 7A + 14

Now we expand the brackets, by multiplying both the 9 and the 2A by the 6 that is outside the brackets.

6x9= 54  and  6x2A=12A

so 12A + 54 = 7A + 14

we must get all the 'A' values on the left and all the other numbers on the right of the equal sign. when you swap sides you change the sign...

12A - 7A = 14 - 54
         5A =  -40

so A = (-40)  divided by 5

(-40) ÷ 5 = -8

so the number is -8

Ais the answer for your question