SOLUTION: Please help me by answering this question: why minus and minus makes plus?

Question 190319: Please help me by answering this question: why minus and minus makes plus?

Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Here's one way to look at it: Let's say that we choose the number 10. It's opposite is -10 (since 10-10=0). So what the minus sign "-" is really doing is changing the given number to it's opposite. Now, if I add another minus sign to -10 to get -(-10), this just asks: what is the opposite of -10? Well since the opposite of 10 is -10, this means that the opposite of -10 is 10 (just flip the two). If you draw a number line and plot 10 and -10, you'll see that they are like mirror images of one another. All that minus sign does is mirror 10 to -10 and -10 to 10.

So this means that -(-10) = 10

So for ANY number "x", we can say that -(-x) = x

If your mind is more oriented towards English, then think of two minus signs as a double negative. So if I say "I do not hate math", then I'm also saying "I do not not like math" or more simply "I do like math". So the two minus signs simply "cancel out".
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Please help me by answering this question: why minus and minus makes plus?
.
Proof:
Let a and b be any real numbers.
Let x=ab+(-a)(b)+(-a)(-b)
.
x= ab+(-a)[(b)+(-b)] factor out -a
=ab+(-a)(0)
=ab+0
=ab
.
x=[a+(-a)]b+(-a)(-b) factor out b
=0*b+(-a)(-b)
=0+(-a)(-b)
=(-a)(-b)
.
x=ab=(-a)(-b)
So, (-a)(-b)=ab
.
Ed

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