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

Question

find the number

Answer 1

step by step:

twice a number, we can call the number n, means two times n, or 2*n.

is equal to comes next so we have 2*n =

then three times the sum of, so we use parentheses to capture that sum:  2*n = 3* (  +  ) 

sum of a number should say 'sum of THE number' so we can use the same n.  so we'll use (n + 2) for that

putting that into the equation above it, we find 2*n = 3*(n + 2)

next, distribute that 3 by multiplying, so you get 2*n = 3*n + 3*2, so

2n = 3n + 2

get all variables on one side.   Subtract 2n from both sides is one way to do it.  2n - 2n = 3n + 2 - 2n

then 0 = n + 2.  Now subtract 2 from both sides to solve for n.  You can finish that off i'm sure :)

 

You could also subtract 3n from both sides, then you would have a negative in front a n,  this is fine.  just be sure to divide by -1 on both sides as the final step.

 

Good luck!