help solving a problem step by step.

Question

I am having trouble understanding problems like this one, 5m - 2[ 3(4m-5) - (m+4)] = 4m + 4 I tried to figured it out on my own but I just don't know how to solve this one and others like this. please help me solve this step by step and explained how to go about solving others like that one.

Answer 1

5m - 2[ 3(4m - 5) - (m + 4)] = 4m + 4

 

5m - 2[ 12m - 15 - m - 4] = 4m + 4

 

5m - 2[ 11m - 19] = 4m + 4

 

5m -22m + 38 = 4m + 4

 

-17m + 38 = 4m + 4

 

-17m - 4m = 4 - 38

 

-21m = -34

 

m = 34/21

 

Answer 2

Always simplify parentheses first.  PEMDAS 

 

[ ] count as parentheses.  so right now only focus on [3(4m - 5) - (m+4)].  To simplify this we have to simplify the inner parentheses.  We can distribute the 3 and also distribute the minus sign to the second parentheses. PEMDAS

 

Which will give us [12m -15 - m - 4]. 

 

** our goal there was to basically get a line of terms being added or subtracted. Also watch out for the  - 4 at the end, many people will miss that and leave it + 4.  They also do not distribute the 3 correctly and write 12m - 5, instead of 12m - 15.

 

Combine like terms within the [  ].  ** We are still focusing on simplifying the [ ], nothing else matters right now. PEMDAS

 

[12m - 15 - m - 4] ---> [11m - 19], and this is as simplified as possible.

 

So going back to the modified original equation 5m - 2[11m-19] = 4m + 4

 

[ ] are parentheses but more importantly it is being multiplied by 2 (minus 2 actually)

 

so by PEMDAS we can distribute (which is multiplication) 5m - 22m +38 = 4m + 4.  **again watch out for distributing the minus sign and the 2 to the 19.

 

PEMDAS the left side since the right side is already simplified.  -17m + 38 = 4m +4

 

Now we solve(we've really only been simplifying up to this point)

 

Remember anything we do to the left side we do to the right side.  When moving terms from one side to the other we use the opposite(or inverse) operation of the operation that it is currently performing with its side.

 

There are different ways to go about it.  I'm going to move my 4m to the left side.  so to do this I subtract it from BOTH sides since it is a positive term.  Watch:  

 

-17m + 38 -4m = 4m +4 - 4m

which becomes -17m + 38 -4m = 4m +4 - 4m

and we get -21m +38 = 4

 

Now move everything away from m one at a time starting with the 38.

 

-21m +38 - 38 = 4 - 38  ---->    -21m +38 - 38 = -34

 

we are left with -21m = -34.  Since it is saying -21 times m, then to move the -21 away we do the opposite operation which is divide to BOTH SIDES.

 

-21m / -21 = -34 / -21

 

-21m / -21 = -34 / -21 -----> m = -34/-21 = 34/21