3n - 2(2n-3) - 3(n + 2)?

Question

please show the step by step

Answer 1

3n - 2(2n - 3) - 3(n + 2)
= 3n - 4n +6 - 3n - 6
= -4n

Answer 2

3n - 2(2n-3) - 3(n + 2)

First, get rid of those blasted, distracting subtraction things.

3n + (-2)[2n + (-3)] + (-3)(n + 2)
I know it looks worse, but it will help you keep track of signs. There's another reason too. a+(-b)=(-b)+a ALWAYS, but relatively seldom does a-b=b-a.

Applying the distributive property: a(b+c)=ab+ac. If you don’t know this, you really ought to learn it.
3n + (-2)[2n + (-3)] + (-3)(n + 2)= 3n + (-2)(2n) + (-2)(-3) + (-3)(n) + (-3)(2)

And, doing some arithmetic…
= 3n + (-4)n +6 + (-3)n + (-6)

Applying the commutative and associative properties of addition: a+b=b+a and (a+b)+c=a+(b+c) respectively… all these do is let us add stuff in any order. You ought to learn these too.
= 3n + (-3)n + (-4)n + 6 + (-6)

Applying the distributive property again…
= [3 + (-3) + (-4)]n + [6 + (-6)]

Will you concede that 3 + (-3)=0, that 0+(-4)=(-4), and 6 + (-6)=)? If so, then that leaves
-4n, So

3n - 2(2n-3) - 3(n + 2) = -4n

Answer 3

3

Answer 4

3n - 2(2n-3) - 3(n + 2)
= 3n - 4n + 6 - 3n - 6
= -4n

Answer 5

3n - 4n + 6 - 3n - 6 = - 4n