First Time on Fourms: Need help with problem explantion. Easy Linear Function

socialdebacle

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Apr 30, 2015
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Hello, I'm a highschool drop out, wanting to pickup math again. I bought E-Z Algebra 2 (Barron's E-Z Series) to start, since I passed Algebra 1.
Sadly I'm stuck on one of the first section excercises, where there are no solutions only an answer in the back of the book.

The problem is a Linear Function.

xx-2
---=---
x+6x


The solutions page at the end of the book is: x = 3.

If someone can please show the methods used to get the answer, it would help a speed up my understanding of numbers.

Thanks to all!
 
Hi.

The given equation shows two algebraic ratios (fractions) that are equal.

Here's a basic rule (shown symbolically) that is useful when two fractions are equal.

A/B = C/D means that A*D = B*C

(The asterisks are multiplication symbols; we don't use the letter x for that, anymore.)

This rule is useful because it provides an equivalent equation in which the fractions have been eliminated.

Here's a way to type the given equation, using grouping symbols.

x/(x + 6) = (x - 2)/x

If we apply the rule above to your equation, we get the following equivalent equation.

(x)(x) = (x + 6)(x - 2)

Simplification initially leads to

x^2 = x^2 + 4x - 12

Then

0 = 4x -12

4x = 12

Questions?

Cheers :cool:
 
Last edited:
The problem is a Linear Function.

xx-2
---=---
x+6x
I can see why you'd be confused: this isn't actually any sort of function, and it isn't any sort of linear anything! :shock:

To learn about solving rational equations, try here.

Once you studied at least two lessons from the listing at the link, the solution provided in a previous reply should make sense. ;)
 
Thanks to both otis and stapel. Otis your explanation was perfect, thanks a buch I've been sadly stuck for a couple of days. Stapel thanks for the reference, I actually came across these video but it didn't take a look because it wasn't under Linear Functions. Well I can't blame the book since this is the review Chapter, Thanks for clearing some stuff up for me.
 
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