SOLUTION: if 2 is subtracted from a number and this difference is tripled, the result is 6 more than the number. find the number.

Question 97614: if 2 is subtracted from a number and this difference is tripled, the result is 6 more than the number. find the number.
Found 3 solutions by checkley71, stanbon, bucky:
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
3(X-2)=6+X
3X-6=6+X
3X-X=6+6
2X=12
X=6 ANSWER.
PROOF
3(4)=6+6
12=12

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
if 2 is subtracted from a number and this difference is tripled, the result is 6 more than the number. find the number.
-----------
Let "x" be the number.
EQUATION:
3(x-2) = x+6
3x-6 = x+6
2x = 12
x = 6
==============
Cheers,
Stan H.
Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
The words "a number" in the problem imply that you are to find an unknown number. Call that
number x.
.
The problem says "if two is subtracted from a number ... ". Translating this into an expression
is done by subtracting 2 from the unknown number x. In algebraic form this is:
.
x - 2
.
This is the difference. The problem says to triple this difference. And in algebraic form
this tripling is:
.
3(x - 2)
.
This tripled form is 6 more than the number. So if we take 6 from this tripled form the
result will equal the unknown number. Or in equation form:
.
3(x - 2) - 6 = x
.
Do the distributed multiplication on the left side by multiplying each of the two terms
inside the parentheses by the multiplier 3. When this multiplication is done you have:
.
3x - 6 - 6 = x
.
Combine the two -6 terms on the left side to make the equation become:
.
3x - 12 = x
.
Subtract x from both sides and the equation becomes:
.
2x - 12 = 0
.
Next get rid of the -12 on the left side by adding 12 to both sides. On the left side the
added 12 cancels the - 12 and the equation then becomes:
.
2x = 12
.
Finally divide both sides by 2 which is the multiplier of the x to reduct the equation to:
.
x = 12/2 = +6
.
The answer is that the unknown number is +6.
.
Let's check this answer by substituting it back into the original problem.
.
First, if you subtract 2 from x you get 6 - 2 = 4.
.
Next if you triple that you have 3 times 4 which equals 12.
.
According to the problem this result is to be 6 more than the number. Is 12 actually 6
more than 6. Yes, it is so the answer checks.
.
Hope this helps you to understand the problem.
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