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