Understanding and Solving Basic Algebraic Equations

[Ottahhh]

Hi, I'm having some trouble understanding how to tackle this question, I would appreciate it if some one could enlighten me on how to do this step by step and as in depth as possible.
It may seem simple to some, but I am fairly new to this sort of equation.

The equation is:
−5[−2(m − 3n) + 4n]

Josh, 13.

 

[Adyssa]

You want to get rid of the brackets, basically, remember the order of operations (BODMAS) - here's a refresher:

http://www.mathsisfun.com/operation-order-bodmas.html

Just to get you started, let's do the first step:

-5[((-2 * m) + (-2 * -3n)) + 4n]

now, you should perform the multiplications inside the two inner brackets, which will leave you with -5[terms from expanded brackets], and you must multiply everything in those brackets by the -5

 

[pwsnafu]

Ottahhh, we aren't allowed to just hand you the answer, but we can guide you step by step.

Oh, and −5[−2(m − 3n) + 4n] is not an equation. What you have there is an expression. An equation is "expression = expression".

 

[Deveno]

another way of thinking about BODMAS/PEDMAS is "inside-out":

we want to get the "innermost" parentheses to go away first:

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

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

which is a consequence of the distributive law

(the distributive law is your friend, give it some love).

to take the next step, you have to use "the rules of sign":

(-a)(-b) = ab
(-a)(b) = -ab
(a)(-b) = -ab
(a)(b) = ab

(sometimes recited as a chant:

"positive times positive is positive, positive times negative is negative, negative times positive is negative, negative times negative is positive"

ok, now just the people on the right:)

 

[Ottahhh]

Okay, so after all your help, I think I have an answer.

How I got my answer:
I started by focusing on the middle, we have -2 (m-3n) + 4n, I'm going to go
-2 x - 3n, as deveno pointed out, 2 negative make a positive so -2 x - 3n = 6n, I'm then going to do -2 x m which will give me -2m so after them sums I have -2 (m + 3n) = -2m + 6n. I can't forget about the 4n so I must do [-2m + 6n + 4n] = [-2m + 10n]. I will then handle the -5, First off I must do -5 x -2m, 2 negatives give me a positive so I will get 10m as my answer. I must then do -5 x 10n which gives me -50n so after those 2 sums, I have -5[-2m + 10n] = 10m - 50n.
Therefore my answer is 10m - 50n, please inform me of If I have gone wrong somewhere along the lines and consequently my answer is wrong.

Josh

 

[micromass]

Ottahhh, can you post this in the homework forum next time: https://www.physicsforums.com/forumdisplay.php?f=155

Thanks!

 

[Ottahhh]

This isn't homework :p This is me having a genuine interest in learning new Mathematical methods.

 

[micromass]

This isn't homework :p This is me having a genuine interest in learning new Mathematical methods.

Yes, but it doesn't really matter if it's homework or not. You're trying to solve math exercises, and such things always belong in the homework forum here.

 

[Ottahhh]

Yes, but it doesn't really matter if it's homework or not. You're trying to solve math exercises, and such things always belong in the homework forum here.

As you wish (: