Simplifying (again) and Graphing ?!?

Question

Blah, okay. Now I only have a problem with 3 more simplifying problems.

1. -7(-2a+b)-(-3b)

Okay so, like, it'd be 7(-2a+b)+ 3b... what else?

Explain that, thank you..

Next is:

2. 1/2 (-72)(4x)

1/2 is a fraction. Explain this one too...

and lastly for simplifying:

3. -1/3(9x - 6y + 12)

Also, explain this one. -1/3 = a negative 1/3 fraction.

I apologize for asking simplifying questions over and over. I've totally forgotten how to do all of it... so bare with me. x];;;

Also for the graphing... when they ask a question like:

"Graph the given numbers on a number line: 2, 1/2, -1 1/3, 0, 3/2"

How would you graph them?

Answer 1

1.) -7(-2a+b)-(-3b); to simplify this you would first multiply the -7 through the (-2a + b) and the - 1 through the -3b

Therefore:

-7(-2a) + -7(b) + -1(-3b)

14a - 7b + 3b

Now combine like terms:

14a - 7b + 3b

14a - 4b

That is your answer.

2.)  1/2 (-72)(4x)

First multiply - 72 by 4x

1/2 (-72)(4x)

1/2 (-288x)

Then either multiply by (1/2) or divide by 2.  Either way it is the same.

-288x/2 = -144x  or (1/2)*(-288x) = -144x

3.)  -1/3(9x - 6y + 12)

First, multiply the (-1/3) through.  You can do this by either multiplying each term by (-1/3) or by dividing each term by -3.

-1/3(9x) - (-1/3)(6y) + (-1/3)(12)

-3x + 2y - 4

or

{[(9x)/(-3)] - [(6y)/(-3)] + [(12)/(-3)]}

-3x - (-2y) + (-4)

-3x + 2y - 4

See, its the same thing.

When you have to graph numbers on a number line, that usually means you:

1.) draw a line

2.) put tick marks on it

3.) number the tick marks

4.) place colored in circles on the numbers the question calls for.

For example:

You had the numbers 2, 1/2, -1 1/3, 0, 3/2

It would look like this:

<--I--I--I--I--I--I--I-->

and then there would be numbers under each mark, the first being -2, then -1, then 0, then 1 and so on.

After that you would place a black dot on the 2 tick, the 0 tick, half way between the 0 and the 1, half way between the 1 and the 2, and 1/3 of the way toward the -2 after the -1 tick.

By the way, you don't have to apologize for forgetting things.  We all do it, especially over the summer. :)