
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 11th, 2018, 12:53 PM  #1 
Newbie Joined: Jun 2018 From: Jordan Posts: 19 Thanks: 0  Some questions related to variables and operations
Hi. I got several algebraic questions and I don't really want them to remain a gap for me. First one is about substituting variables / expressions; Say that we have $\displaystyle (xy)^3=4x$. If I decide to substitute the expression $\displaystyle xy$ with the variable $\displaystyle n$, which is the new correct form of the utter expression? 1 $\displaystyle n^3 = 4x $ 2 $\displaystyle n^3 = 4n/y$ (assuming $\displaystyle x = n/y$) 3 Both The next question is, If I substitute a variable with an expression, do I have to do it everywhere? For example; Say that $\displaystyle y = 3x$ and $\displaystyle g * \sqrt{y} = 2y$ Can it be $\displaystyle g*\sqrt{y} = 6x$ ? Another question ; If I were to multiply / divide a fraction by a value that has many forms, can I use different forms for certain purposes? Say I want to multiply $\displaystyle \frac{x}{y}$ with 1, but also $\displaystyle \sin^2(x) + \cos^2(y) = 1$. is this correct? $\displaystyle \frac{x}{y} = \frac {x(\sin^2(x)+\cos^2(x))}{y} $ Last question ; is the above case possible when it comes to equations too? For example, assume that $\displaystyle g+c = 3 $ and I have the equation: $\displaystyle 3x^2 = y $ If I multiply both sides by 3, but in 2 different forms $\displaystyle 9x^2 = y(g+c) $ is this correct? ^ Thanks in advance. Last edited by skipjack; August 15th, 2018 at 04:33 AM. 
August 11th, 2018, 01:22 PM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,197 Thanks: 1152  Quote:
Quote:
Can you? Sure, equality is equality. If two elements are equal, you can freely substitute one for another. Quote:
Quote:
Last edited by skipjack; August 15th, 2018 at 04:38 AM.  
August 14th, 2018, 02:03 AM  #3 
Newbie Joined: Jun 2018 From: Jordan Posts: 19 Thanks: 0 
Thanks!

August 14th, 2018, 05:31 AM  #4  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,592 Thanks: 953  Quote:
 
August 15th, 2018, 02:39 AM  #5 
Newbie Joined: Jun 2018 From: Jordan Posts: 19 Thanks: 0  Yep I know that it would give the same answer but my question wasn't whether it would be the same in terms of value or not. All I wanted to know is whether is it permissible to do such operations or not. (For e.g: having a new variable in terms of 2 subvariables and then using it along with another subvariable in the same expression such as my first example)


Tags 
operations, questions, related, variables 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Two questions related to normal distribution  wajeeha yasin  Probability and Statistics  1  December 31st, 2016 01:49 PM 
Area related questions  Drunkuncito  Calculus  4  June 23rd, 2016 04:59 PM 
Rational Numbers and Operations Questions  gabbe  Algebra  2  March 14th, 2010 05:10 PM 
Order of operations  parenthesis with 3 variables each  mathmonkey  Elementary Math  3  July 28th, 2009 12:33 AM 
please dont post questions not related to algebra  kaulabhishek_862  Abstract Algebra  1  June 25th, 2008 08:03 AM 