The sum of 6 and twice a number is multiplied by three. This product is greater than or equal to 66. What is the smallest value possible for this number?

Question

espex · Answer

Your first step will be to write a mathematical equality to represent the word in your problem.

whpalmer4 · Answer

Build it up piece by piece.  Let $n$ be your number.  Twice a number would be $2n$.  The sum of 6 and twice a number would be $6 + 2n$.  The sum of 6 and twice a number is multiplied by three would be $(6+2n)*3$.  That product is $\ge$ 66.  Combine that all together and what do you get?  

Once you have your number sentence / inequality, it's time to solve it.  Add, subtract, multiply, divide as necessary to get it in the form $n \ge x$ where $x$ is your answer for the smallest possible value.  You can do any of those operations provided that you do the same thing to both sides of the equation.  Don't divide by 0, however, and if you multiply or divide by a negative number, you change the direction of the inequality sign.