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?

For these type of questions, it requires you to understand and write a algebraic equation out of words given.

Therefore, let that number be y.

"if 9 is added to twice a number" = 2y + 9
"this sum is multiplied by six" = (2y + 9) x 6

"the number is multiplied by 7" = 7y
"14 is added to the product" = 7y + 14

Now combine the expressions and solve away!

(2y + 9) x 6 = 7y + 14

Expand.
12y + 54 = 7y + 14

Shift all the y to a side and all the pure numbers to another side.
12y - 7y = 14 - 54

Group them.
5y = - 40

Divide 5 on both sides.
y = - 8

Therefore, the number is - 8.