SOLUTION: PLEASE HELP...IF YOU DOUBLE A NUMBER AND THEN ADD 12, YOU GET ONE HALF OF THE ORIGINAL NUMBER. WHAT IS THE ORIGINAL NUMBER?

Click here to see ALL problems on real-numbers

Question 494026: PLEASE HELP...IF YOU DOUBLE A NUMBER AND THEN ADD 12, YOU GET ONE HALF OF THE ORIGINAL NUMBER. WHAT IS THE ORIGINAL NUMBER?
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Let x be the original unknown number.
.
Double that number means taking 2 times x which is written as 2x.
.
Then add 12 to that and you have 2x + 12
.
The problem tells you that this should equal 1/2 of the original number, or (1/2)x
.
Setting these two quantities equal results in the equation:
.
2x + 12 = (1/2)x
.
You can get rid of the fraction on the right side by doubling both sides of this equation ... Do that by multiplying both sides (all terms) by 2 and the equation becomes:
.
4x + 24 = x
.
Subtract x from both sides:
.
3x + 24 = 0
.
Then subtract 24 from both sides:
.
3x = -24
.
Finally solve for x (the original number) by dividing both sides of this equation by 3 to get:
.
x = -24/3 = -8
.
So the answer is that the original unknown number is -8.
.
Check it out. Double it to get -16 then add 12 to the -16 and the result is -4. This checks because it is supposed to equal half the original number which is one-half of -8. And it does.
.
This checks the answer. The original number is -8.
.
Hope this helps you to understand the problem.
.