2(2–3r)=–5(r–3)

Question

1. Hello I'm Chrissy I have a hard time in math class.I'm looking for help, I find this website I hope I can find the help I need thank you

Answer 1

Hi Chrissy,

 

I'm Mark (I'm an Engineer who used to work on the Space shuttle so I think I can get you through this.)

 

You said your having trouble understanding this

 

2(2–3r)=–5(r–3)

 

Your goal is to

1) distribute the 2 and the -5

2) combine "Like Terms" (terms with r in them, and terms with just numbers)

3) solve for r

 

 

That you asked this question tells me a few things

 

1.) you are probably having trouble understanding what is called the "Order of Operations."

 

I want you to please LOOK THAT UP on Wikipedia   https://en.wikipedia.org/wiki/Order_of_operations

 

"...Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS is often expanded to "Please Excuse My Dear Aunt Sally", with the first letter of each word creating the acronym PEMDAS."

 

You should also find it explained in your Text Book.

You NEED to learn all about PEMDAS and how to use it.

 

 

 

2.) you may also be having a problem understanding the "Distributive Law"

 

When you see this 2(2–3r)=–5(r–3)   the first thing you should notice are the numbers multiplying each SET of Parentheses. Lets start with just the left side first...

 

I am going to "DISTRIBUTE" the 2... watch how I do:

2 times the first TERM in the parentheses + 2 times the SECOND TERM (Include the - sign !!!)

 

HINT:  2 - 3r  =  (2) + (-3r)

 

2(2–3r) =  2 ( (2) + (-3r) )

            =  2(2) + 2(-3r)

            =  4 + (-6r)

            =  4 - 6r          Now the left side has been distributed and is in individual TERMS

 

You may also be having problems getting USED to the Parentheses and how we use them to IMPLY Multiplication.

 

2(2-3r) MEANS "2 times THE QUANTITY ( 2 - 3r)" or 2 times the 2 AND 2 times the  -3r

 

 

________________

 

NOTE: IF it helps you can draw two arrows to remember the distribution. I cant do it here, but I can explain how

 

2 ( 2 -3r )

 

Start on top of the first 2.  Draw a curved line up and over the first parentheses and down to the top of the second 2

 

Then for the second arrow, start in the same place and draw a longer curved line up and over to the -3r term

 

This can help you remember to distribute properly, but eventually you wont need to do that.

_______________

 

 

so here is where we were...

 

 

2(2–3r)=–5(r–3)

 

Left side

 

2(2–3r) = 2 ( 2 + (-3r) )
= 2(2) + 2(-3r)
= 4 + (-6r)
= 4 - 6r

 

Now lets do the right side

 

–5(r–3)  = (-5)( r + (-3) )       I like to re-write subtraction terms like  r-3  as  r+(-3)  to help keep signs right.

             = (-5)(r) + (-5)(-3)    See how this makes it clear you need to multiply two negative numbers?

             = -5r + 15                 NEG 5  times NEG 3 equals POS 15

 

if you had trouble with the Negative numbers then your going to need to get help with that.

or if you are having problems with the use of Parentheses and Distribution that is a separate thing to get help with

 

We found    2(2–3r)  =  4 - 6r
and            –5(r–3)   = -5r + 15

So now we can substitute in our term expansions

 

2(2–3r)=–5(r–3)

4 - 6r = -5r + 15

 

OR we could have done it ALL AT ONCE ON BOTH SIDES... 

 

Eventually this is how your paper will look once you are good at this

 

2(2–3r)  =  –5(r–3)

2 ( 2 + (-3r) )  =  (-5)( r + (-3) ) 

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

4 - 6r = -5r + 15        

 

SO NOW we are at a critical point - We must "COMBINE LIKE TERMS"

 

IF you have trouble with THIS part it is because you need help in MOVING TERMS from one side of an Equation to the other.  Another way to say that is You need help "MANIPULATING Equations."

 

First, you need to remember that the Variable goes to the Left and the numbers to the RightThat way your Answer will look like this:

 

r = Ans.  So lets start by moving the -5r term to the left side, see if you can keep up :)

 

4  -6r  =  -5r  +15

    +5r     +5r            Remember!  What you do to One side of an Equation you must do to the OTHER as well !!!

 

4  -1r   =  0r   +15

 

4    -r   =        +15

-4                     -4 

0     -r  =        +11

 

So...

-r  = +11

 

multiply both sides by -1

 

-1 (-r  = +11)

-1(-r) = -1(11)

 

r = -11

 

Now lets Check our Answer.

 

2( 2 –3r ) = –5( r –3 )

2( 2 -3(-11) ) = -5( (-11) -3 )     Substitute for r = -11

2( 2 +33 ) = -5( -14 )                start from the inner most parentheses and work out

2 ( 35) = -5 ( -14 )

+70 = +70  CHECK !!!

ANS  r = -11          Circle that ANSWER !!! :)

 

 

 

Answer 2

2(2–3r)=–5(r–3)

 

You want to "solve for r"; that is, you want to find the value of r:

 

     2(2–3r) = –5(r–3)

 

Multiply out the terms on each side:

 

     4 - 12r = -5r + 15

 

Add 12r to both sides:

 

     4 = 7r + 15

 

Subtract 15 from both sides:

 

     -11 = 7r

 

Divide both sides by 7:

 

    -11/7 = r