SOLUTION: Twice the difference of a number and 9 is equal to three times the sum of the number and 4. Find the number

Algebra.Com
Question 1161810: Twice the difference of a number and 9 is equal to three times the sum of the number and 4. Find the number
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

2*(x - 9) = 3*(x+4)


2x - 18 = 3x + 12


-12 - 18 = 3x - 2x


   x = -30.    ANSWER

Solved.

----------------

Regarding the post by @josgarithmetic,  giving two solutions/answers  6  and  -30,
keep in mind,  that his answer 6 is wrong.


Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
The description tells you what to do.

.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


The expressions are linear; there will not be two different answers.

The problem with the solution by tutor @josgaritihmetic is that it uses two different interpretations of "the difference of a and b".

In everyday language, a difference is nearly always assumed to be a positive number. For example, if a man is 40 and his wife is 35, then the difference of the man's age and the wife's age is 5 years, and the difference of the wife's age and the man's age is 5 years.

But in mathematics, you can't have two different interpretations of "difference".

Mathematically, the difference of the man's age and his wife's age is 5; the difference of the wife's age and the man's age is -5.

In other words, mathematically, the difference of A and B is ALWAYS A-B; it is NEVER B-A.
RELATED QUESTIONS

Twice the sum of a number and 9 is equal to three times the difference of the number and... (answered by thejackal,ewatrrr)
twice the sum of a number and 5 is equal to three times the difference of the number and... (answered by algebrahouse.com)
twice the sum of a number and 9 is equal to three times the difference of the number and... (answered by ReadingBoosters)
Twice the sum of a number and 8 is equal to three times the difference of the number and... (answered by rfer,algebrahouse.com)
Twice the difference of a number and 6 is equal to three times the sum of the number and... (answered by rapaljer)
Twice the difference of a number and 8 is equal to three times the sum of the number and... (answered by mananth)
twice the difference of a number and 8 is equal to three times the sum of the number and... (answered by stanbon)
twice the sum of a number and 8 is equal to three times the difference of the number and... (answered by mala_kumarkos@yahoo.com)
twice the difference of a number and 3 is equal to three times the sum of the number and... (answered by bucky)