twice the difference of a number and 2 is equal to three times the sum of the number and 4

Question

 i'm stuck

Answer 1

First assign a variable to the number.  Call it x.

 

Now follow exactly what the problem says:

 

"twice the difference of a number and 2" -- that's 2 (x - 2) (though that's ambiguous -- see below)

"is equal to" -- in other words, =

"three times the sum of the number and 4" -- 3 (x + 4)

 

So there's an equation, which can be solved easily:

 

2 (x - 2) = 3 (x + 4)

2x - 4 = 3x + 12

2x = 3x + 16

-x = 16

x = -16

 

HOWEVER...  Maybe "the difference of a number and 2" means 2 - x, and not x - 2.  What happens then?

 

2 (2 - x) = 3 (x + 4)

4 - 2x = 3x + 12

-8 - 2x = 3x

-8 = 5x

 

In this case the answer would be -8/5, which is probably not what they wanted.