Understanding and Solving Functions to Solving Complex Equations

[melvinator]

I am having a hard time understanding how to solve functions.I am working on the following problem

Given the equation (y-x/6) - (3x-y/9) = 4 - (x+2y/4) + (x+4y/12)

g(y) is .....?

Homework Equations

The Attempt at a Solution

 

[symbolipoint]

Your problem description does not give any information about g(y); and does not show in any way how g(y) is related to the equation. If "x" is the variable for the x-axis and "y" is the variable for the y-axis, then g(y) is a relation and not a function. Are you hoping to find the relation x=g(y) ?

EDIT: actually, without going through the solution (likely) process, I should not say that g(y) is not a function; it may well be one but we do not know until we try to solve the equation for x.

 

[melvinator]

That is exactly how the problem is presented in the text.Below are the 4 answer choices I am given.Maybe they will give some clue as to what they want.

1. 0.632x+12
2. 0.750y+12
3. 1.333y-12
4. 1.333x-12

 

[Mark44]

The equation is linear in x and y, so the equation is of a line. Since the problem asks for g(y), I interpret this to mean that it asks you to solve for x in terms of (as a function of) y. Collect all of the terms involving x on one side, and all of the terms involving y on the other side.

After working this problem, I don't get any of the answers you show, which leads me to believe that you have not given us the problem as it appears in your book.

You wrote

(y-x/6) - (3x-y/9) = 4 - (x+2y/4) + (x+4y/12)

Most of the people in this forum interpret the expression in the first pair of parentheses as
$$y - \frac{x}{6}$$
and similarly for the other parenthesized expressions.

Does this expression appear in your text in this way:
$$\frac{y - x}{6}$$
?
These are not the same. If you don't know how to use LaTeX, you need to put parentheses in the right places. For example, the expression just above should be written as (y - x)/6. The same goes for all of the other expressions in parentheses.

 

[melvinator]

Please forgive me,this is my first post.Below is the equation in the correct format

(y-x)/6 - (3x-y)/9 = 4 - (x+2y)/4 + (x+4y)/12

 

[symbolipoint]

You are apparently looking for an expression for x. Your equation given uses rational expressions. Clear the fractions by multiplying both sides by the lowest common denominator. The rest will be uncomplicated simple algebra.