My Math Forum Solving Literal Equations and Absolute Value Equations:

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 July 28th, 2009, 02:24 PM #1 Member   Joined: Sep 2008 Posts: 97 Thanks: 0 Solving Literal Equations and Absolute Value Equations: I just started learning about literal equations today and i'm confused, could anyone tell me step by step how to solve literal equations and literal equations containing fractions? Example: Solve 1/x = 1/y for x Also, I'm working on Absolute Value Equations and the chart is a little confusing a step by step guide on it would be great too! Example: Solve |3x+4|=13 I'm cramming for the GED and i think i'm about 2/3's of the way though any help you guys could give me would be great Thanks!
 July 28th, 2009, 03:21 PM #2 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Re: Solving Literal Equations and Absolute Value Equations: First example: Solve $\frac{1}{x}= \frac{1}{y}$ for $x$. $1= (\frac{1}{y})(x)$, then $x= \frac{(1)}{(\frac{1}{y})} = y$. Also notice that both $x$ and $y$ cannot equal to zero. Second example: Solve $|3x+4|= 13$. $3x+4= 13$ and $3x+4= -13 \longrightarrow \therefore x = 3$ and $x= -\frac{17}{3}$.
 July 29th, 2009, 08:17 AM #3 Member   Joined: Sep 2008 Posts: 97 Thanks: 0 Re: Solving Literal Equations and Absolute Value Equations: Ok i understand the second one but the first one still confuses me a little bit..
July 29th, 2009, 08:51 AM   #4
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From: Sacramento, California

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Re: Solving Literal Equations and Absolute Value Equations:

Quote:
 Originally Posted by cafegurl Ok i understand the second one but the first one still confuses me a little bit..
You have three ways you can solve this:
[1] You can multiply both sides by x and then by y.
$\frac{1}{x}=\frac{1}{y}$

$x\cdot \frac{1}{x}=x\cdot \frac{1}{y}$

$1=\frac{x}{y}$

$y\cdot 1=y\cdot \frac{x}{y}$

$y=x$

$x=y$

[2] Solve it like a proportion.
$\frac{1}{x}=\frac{1}{y}$

$x=y$ (cross multiply)

If the reciprocals of two numbers are equal then the two numbers have to be equal, right?

 August 1st, 2009, 08:29 PM #5 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Only three ways, SidT? Another way to solve this one is to subtract both sides by 1/y, then we do some algebra and get (y - x) / xy on one side of the equation, and then multiply both sides by xy, and add by x to both sides and we get x = y, where both x and y cannot equal to zero!
 August 1st, 2009, 10:44 PM #6 Global Moderator   Joined: Dec 2006 Posts: 18,956 Thanks: 1603 Dividing 1 by each side of the equation gives x = y.
 August 3rd, 2009, 07:58 AM #7 Senior Member   Joined: May 2008 From: Sacramento, California Posts: 299 Thanks: 0 Re: Solving Literal Equations and Absolute Value Equations: Well, there's probably more, but those are the ones that came to my mind.

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