CORE 1, Expanding and Simplifying - HELP?

There's a question in my textbook:

$$5x-6-(3x-2)$$

I think I misunderstood as I put the following for my working out:

$$5x-6-3x-2$$

And from that I got:

$$2x-8$$

Can anyone help me to understand how to get the right answer?

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When you subtract (3x-2), you need to change the sign on both 3x and -2. So $5x - 6 - (3x - 2) = 5x - 6 - 3x + 2$. – Adam Saltz Sep 22 '11 at 17:35

1 Answer

Think of subtracting the quantity in the parentheses as a application of the distributive power. Consider that: $$5x-6-(3x-2) = 5x-6+(-1(3x-2))$$ As adding a negative is the same as subtracting a positive. Then, just distribute the -1 over the quantity in parentheses so:$$5x-6-(3x-2) = 5x-6+(-3x+2))$$ As the -1*-2 becomes a +2 and the -1(3x) is merely -3x. Now, as there's nothing multiplying the quantity in parentheses, you can simply take them off and get:$$5x-6-(3x-2) = 5x-6-3x+2$$ Hopefully that clarifies things for you, but feel free to comment if something is unclear.

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