Both are saying the same thing.

-2(5) - 7(-3)

You are taking the - 7 similar to:

-2(5) + (-7)(-3)

to get:

-10 + 21 = 11

Which is fine.

I think the book you are using wants you to keep the 7 as a positive number that is getting subtracted:

-2(5) - 7(-3)

-10 - (-21)

and since subtracting a negative is the same as adding its opposite:

-10 + 21 = 11

you get the same answer anyway. Two different ways to think of the same problem, and both are correct ways of thinking.

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Looking back, you end up with:

-10 - (-21) = -11

which is just wrong, as the math has you turn the subtraction of negative into the addition of the positive, so the answer is +11. So your thinking is correct, just somehow ended up with a negative number.

Your question is very confusing. You're all over the place.

I'm not sure what you think is correct and what you think is incorrect.

−7(−3) is the same as −(−21) which is the same as +21

−2(5) is the same as −(10) or just −10

−2(5)−7(−3)

−(10)−(−21)

−10+21

11

−2(5)−7(−3) use order of operations ... multiplication is done before addition and subtraction ... also -7(-3) = + (-7)(-3)

= (-2)(5) + (-7)(-3)

= (-10) + 21 <<< now do the addition

= 11 <<< correct answer and correct method

============================ Below is trying to explain your mistakes .... learn the rules for addition, subtraction, multiplication and division of positive and negative numbers ... you are applying those rules wrong.

you said ... 10-(-21)=-11

but 10-(-21) is still not =-11 ... think of the algebraic definition of subtraction ... subtracting is adding the opposite

10-(-21)

= 10 + (+21) = +31

but the 10 should NEVER be positive ...

-2(5) = -10 <<< multiplying 2 numbers with opposite signs is always negative ---- so your method actually has at least 2 mistakes

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Like I said above ... learn the rules ... AND then practice until they becoe easy .... doing something one time is NOT enough ... practicing the rules is the key

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