why does x + -8/9of x = 1/9 of x

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
richie_rich
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Joined: Tue Dec 27, 2016 2:00 pm
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why does x + -8/9of x = 1/9 of x

Hi,

I accept that I'm atrocious at maths so please don't be too harsh

I'm trying to work my way through Bhaskara Lilavati where you work out the number of bees.
The equation is (the square root of x/2 )+ 8/9 of x + 2 = x

So I found an answer and the first 3 steps are as follows:

1.(square root of 1/2 of x) + 8/9 of x + 2 = x

2. add -2 to both sides
(square root of 1/2 of x )+ 8/9 of x + 2 + -2 = x + -2

(square root of 1/2 of x) + 8/9 of x = x -2

3. add -8/9 of x to both sides
(square root of 1/2 of x) + 8/9 of x + -8/9 of x = x - 2 + -8/9 of x
(square root of 1/2 of x) = 1/9 of x - 2?

My question is at step 3 how do you get from x - 2 + -8/9 of x to 1/9 of x - 2
If someone could explain this to me in real simple step by step terms I would be very grateful

little_dragon
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Joined: Mon Dec 08, 2008 5:18 pm
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Re: why does x + -8/9of x = 1/9 of x

The equation is (the square root of x/2 )+ 8/9 of x + 2 = x
I'm taking this to mean:

$\sqrt{\dfrac{x}{2}\,}\, +\, \dfrac{8}{9}\,x\, +\, 2\, =\, x$
So I found an answer and the first 3 steps are as follows:

1.[orig. eqn]

2. add -2 to both sides

3. add -8/9 of x to both sides
I think you did this:

$\sqrt{\dfrac{x}{2}\,}\, +\, \dfrac{8}{9}\,x\, +\, 2\, =\, x$

$\sqrt{\dfrac{x}{2}\,}\, +\, \dfrac{8}{9}\, x\, +\, 2\, -\, 2\, =\, x\, -\, 2$

$\sqrt{ \dfrac{x}{2}\,}\, +\, \dfrac{8}{9}\, x\, =\, x\, -\, 2$

$\sqrt{ \dfrac{x}{2}\,}\, +\, \dfrac{8}{9}\, x\, -\, \dfrac{8}{9}\, x\, =\, 1x\, -\, \dfrac{8}{9}\, x\, -\, 2$

$\sqrt{ \dfrac{x}{2}\,}\, = \, \dfrac{9}{9}\, x\, -\, \dfrac{8}{9}\, x\, -\, 2$

$\sqrt{\dfrac{x}{2}\,}\, =\, \dfrac{1}{9}\, x\, -\, 2$
My question is at step 3 how do you get from x - 2 + -8/9 of x to 1/9 of x - 2
I don't understand
you say that you did these steps but then you say you don't understand the steps???
why did you do that step?
what ELSE did you get when you subtracted 8/9 from 1?
what are the steps (missing from your post) where you got confused?
thnx

richie_rich
Posts: 2
Joined: Tue Dec 27, 2016 2:00 pm
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Re: why does x + -8/9of x = 1/9 of x

Step 3. Add ${\frac{-8}{9}x$ to both sides

$\sqrt{\frac{1}{2}}x \ + \ {\frac{8}{9}}x \ + \ {\frac{-8}{9}}x \ = \ x -2 \ + \ {\frac{-8}{9}x$

The above part after the = sign is equivalent to:

$= \ x \ + \ -2 \ + \ \frac{-8}{9} x$

$= \ (x + \frac{-8}{9}x) +(-2)$

which is equivalent to (and the bit that I was confused about until I realised you turn the x into $\ \frac{9}{9}$ - I did say my maths is atrocious) :

$= \ \frac{9}{9} \ + \ \frac{-8}{9}$

which is the same as the way you put it:
$= \ \frac{9}{9} \ - \ \frac{8}{9}$

both of the above = 0.1111111111 which is the same as $\ \frac{1}{9}$

Thanks for your help and for not being too harsh on me. I should have thought about it a bit longer before I posted something so simple.