SOLUTION: Translate into a variable expression. Then simplify the expression. a number decreased by the difference between nine and the number

Question 1198927: Translate into a variable expression. Then simplify the expression.
a number decreased by the difference between nine and the number
Found 3 solutions by MathLover1, Theo, greenestamps:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

let a number be

a number decreased by the difference between and the number

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
to find the difference, you would subtract the smaller number from the larger number.

if x is larger than 9, then x - (x - 9) = 9

if x is smaller than 9, then x - (9-x) = 2x - 9

example 1:
x is equal to 5
since x is less than 9, you get x - (9-x) becomes 5 - (9-5) which becomes 5 - 4 which becomes 1.

example 2:
x is equal to 15
since x is larger than 9, you get x - (x - 9) which becomes 15 - (15 - 9) which becomes 15 - 6 which becomes 9.

you can also use an absolute value expression.

youc could get x - |x - 9|
if (x - 9) is positive, then this becomes x - (x - 9)
if (x - 9) is negative, then this becomes x + (x - 9)
note that, if x = 15, then (x - 9) is positive and if x = 5, then (x - 9) is negative.
you would get 15 - (15 - 9) = 9 because (x - 9) is positive.
you would get 5 + (5 - 9) = 1 because (x - 9) is negative.

let me know if you have any questions.
theo

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Go with the response from @MathLover1; the response from @Theo is mathematically incorrect.

It is true that, in everyday usage, to find the difference between two number you subtract the smaller from the larger -- resulting in a positive answer for the difference.

But in formal mathematics, the "difference between A and B" is always A-B, even if the result is negative.

For the expression in your post....

"a number decreased by..." --> x- ...

"the difference between 9 and the number: --> 9 - x

"a number decreased by the difference between 9 and the number: --> x - (9 - x) = x - 9 + x = 2x - 9

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