SOLUTION: How do you solve the differences between -3 and a number is 8.find two possible value for the number.

Question 1197031: How do you solve the differences between -3 and a number is 8.find two possible value for the number.
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
-3 - x = 8
subtract 8 from both sides of the eqution and add x to both sides of the equation to get -3 - 8 = x
solve for x to get x = -11
if you do x - -3 = 8, then:
add 3 to both sides of the equation to get x = 8 + 3 = 11
your two answers are x = -11 or x = 11.
the statement "difference between -3 and 8" can be interpreted as "-3 - 8" or "8 - -3".
one way out of the difficulty is to say "absolute value of x = 11".
whether x is equal to -11 or 11, the absolute value is always 11.
the other way out is to use the convention from purplemath.
here's a reference:
a rel=nofollow HREF= "https://www.purplemath.com/modules/translat.htm" target = "_blank">https://www.purplemath.com/modules/translat.htm
here are some examples:
https://www.purplemath.com/modules/translat2.htm
the comments about difference of are shown below:
strart:
translate "the difference of 5 and y" into an algebraic expression.
The keyword here is "difference", telling me that one of the items is subtracted from the other. Since order matters in subtraction, I'll need to be careful with the order of the items. Since the number comes first in the English expression, it will need to come first in the math expression. Then this translates to:
5 − y
end:
note that the statement was the difference of and not the difference between.
i think absolute value of 11 gets rid of the ambiguity and doesn't get into the verbal gymnastics of who came first.
you could also say the difference is -11 or 11.
another way to look at it is via the number line.
-3 is to to the left of 8.
the distance between them is 11, not -11.
in other words, the distance between them on the number line is always a positive value, not a negative value.
i don't know what the experts say.
i'm certainly not one of them.
i would be inclined to say the difference between two numbers is always a positive number unless you specifically say number 1 minus number 2 or number 2 minus number 1.
here's a reference that say to subtract the smaller number from the larger number.
https://www.twinkl.com/teaching-wiki/finding-the-difference
here's another reference.
https://www.mathswithmum.com/difference-between-two-numbers/
i'd go with that, unless otherwise specified.

Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

Technically, the statement of the problem is not valid. It implies that there are two different values for the number that satisfy the conditions; there are not.

I was startled to find the number of internet references that say that the difference between two numbers is always positive (or zero). That might be the common convention in everyday English -- but not in mathematics.

In formal mathematics, the "difference between A and B" means only one thing: A-B. So there is only one answer to "the difference between -3 and a number is 8":

Note that if you use the informal meaning of the difference between two numbers, then the two solutions are NOT -11 and +11, as shown by the other tutor. The second informal solution is

Informally, the two solutions to the problem can be found by interpreting the question as finding the two numbers whose distances from -3 on a number line is 8. Those two numbers are -3+8 = 5 and -3-8 = -11.

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