SOLUTION: If 12 is subtracted from three times a number and the difference is multiplied by 2, the result is -42. Find the number.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If 12 is subtracted from three times a number and the difference is multiplied by 2, the result is -42. Find the number.      Log On


   



Question 106053: If 12 is subtracted from three times a number and the difference is multiplied by 2, the result is -42. Find the number.
Found 2 solutions by Earlsdon, MathLover1:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
From the problem description, you can write: (n = the missing number)
2(3n-12) = -42 "If 12 is subtracted from 3 times a number (3n-12) and the difference is multiplied by 2, (2(3n-12)) the result is (=) -42"
Simplify and solve for n.
2(3n-12) = -42 Apply the distributive property to the left side.
6n-24 = -42 Add 24 to both sides.
6n = -18 Finally, divide both sides by 6.
n = -3

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If 12 is subtracted from three times a number, we can write it as
3x-12
and the difference is multiplied by 2, we can write it as
%283x-12%292

and if the result is -42,we can write it as
%283x-12%292+=+-42
Find the number:
%283x-12%292+=+-42 ---- both sides divide by 2
3x+-+12+=+-21 ---- add %2B12 to both sides
3x+-+12+%2B+12+=+-21+%2B+12

3x+=+-9---- both sides divide by 3
x+=+-3
check:
%283x-12%292+=+-42
%283%2A%28-3%29+-12%292+=+-+42
%28-9+-12%292+=+42
-21%2A2+=+-42
-42+=+-42