The quotient of the difference of sixteen times a number squared and five and the sum of the same number and fourteen (when x=-2)

Question

Translate the verbal sentence into an algebraic expression, then use the replacement value given to simplify the expression

Answer 1

Hi Brain!

 

I like to take translate into algebraic expressions by starting at the beginning. So, lets break it down:

 

"The quotient of" means to divide. I will use a fraction bar to represent division:

 

               / 

 

"the difference of sixteen times a number squared and five" - get ready for the first part of the division problem. The "difference" means to subtract. "Times" means to multiply" and "a number" implies that the number is unknown. Anytime a number is unknown, use a variable:

 

16x² - 5 / 

 

"and the sum of the same number an fourteen" - get ready for the second part of the division problem. The "sum" means to add" the "same number" implies we are using the SAME unknown number, so use the SAME variable as before!

 

16x² - 5 / x + 14

 

Great! Now the expression is set up, we will now plug in -2 wherever we see "x" and simplify:

 

     16(-2)² - 5 / (-2) + 14

=   16(4)    - 5 / (-2) + 14           

=    64       - 5 / (-2) + 14

=    59            / 12

 

The solution is 59/12