Three times a certain number added to 14 is the same when 2 times the number is subtracted from 6. What is the number

Answer 1

Hi George,

The key to breaking down these kinds of problems is turning words into formulas.

"Three times a certain number" -> Three times a number you don't know? Sounds like 3x to me!

"added to 14" -> Pretty straight forward. This is + 14

"is the same when" -> This is your equal sign. So we have one half of the equation. =

"2 times the number" -> Two times our mystery number, meaning simply 2x

"subtracted from 6" -> So it will be 6 -

Put it all together. 3x + 14 = 6 - 2x

Solve:

(1st) Isolate x. Remove the -2x by adding +2x to each side

3x+2x + 14 = 6 -2x+2x -> 5x +14 = 6

(2nd) Isolate your number values by subtracting the 14

5x +14-14 = 6-14 -> 5x = -8

(3rd) Divide by 5 so there is only one x

5x/5 = -8/5 -> x= - 8 / 5

Solution is x = - 8 / 5