Solve for X

• Sep 9th 2009, 02:02 AM
jello
Solve for X
Hello Everyone,

I'm banging my head against the wall trying to solve this complex fraction. Can anyone point me in the right direction or give any hints / tips?

1/((0.25/30)+(0.25/20)+(x/15)+(1-(0.5+x)) = 10

I think what's throwing me off most is how to handle the (1-(0.5+x)); should I still multiply by the LCD?

Thanks!
• Sep 9th 2009, 03:16 AM
Hello jello

Welcome to Math Help Forum!
Quote:

Originally Posted by jello
Hello Everyone,

I'm banging my head against the wall trying to solve this complex fraction. Can anyone point me in the right direction or give any hints / tips?

1/((0.25/30)+(0.25/20)+(x/15)+(1-(0.5+x)) = 10

I think what's throwing me off most is how to handle the (1-(0.5+x)); should I still multiply by the LCD?

Thanks!

You haven't got this expression quite correct - there's a missing right parenthesis somewhere. If it should come just before the = sign, then what you mean is:

1/
((0.25/30)+(0.25/20)+(x/15)+(1-(0.5+x))) = 10

in which case the equation is:

$\displaystyle \frac{1}{\dfrac{0.25}{30}+ \dfrac{0.25}{20}+\dfrac{x}{15}+ \Big(1-(0.5+x)\Big)}= 10$

Multiply top and bottom of the LHS by $\displaystyle 60$, and remove the inner pair of brackets from $\displaystyle \Big((1-(0.5+x)\Big)$, noting the minus sign in front of the $\displaystyle x$:

$\displaystyle \frac{60}{\dfrac{60\times0.25}{30}+ \dfrac{60\times0.25}{20}+\dfrac{60x}{15}+ 60(1-0.5-x)}= 10$

$\displaystyle \Rightarrow \frac{6}{0.5+0.75+4x+60(0.5-x)}=1$

$\displaystyle \Rightarrow \frac{6}{31.25-56x}=1$

$\displaystyle \Rightarrow 6 = 31.25-56x$

$\displaystyle \Rightarrow 56x = 25.25$

$\displaystyle \Rightarrow x = 0.4509$ (to 4 d.p.)

• Sep 9th 2009, 04:00 AM
aidan
Quote:

Originally Posted by jello
Hello Everyone,

I'm banging my head against the wall trying to solve this complex fraction. Can anyone point me in the right direction or give any hints / tips?

1/((0.25/30)+(0.25/20)+(x/15)+(1-(0.5+x)) = 10

I think what's throwing me off most is how to handle the (1-(0.5+x)); should I still multiply by the LCD?

Thanks!

The fraction:
$\displaystyle \dfrac{1}{\dfrac{0.25}{30}+\dfrac{0.25}{20}+\dfrac {x}{15}+(1-(0.5+x)} = 10$

$\displaystyle \dfrac{1}{\dfrac{0.25}{30}+\dfrac{0.25}{20}+\dfrac {x}{15}+ 0.5 - x } = 10$

common denominator
$\displaystyle \dfrac{1}{\dfrac{0.25}{30}+\dfrac{1.5 (0.25)}{1.5(20)}+\dfrac{2x}{2(15)}+ \dfrac{30(0.5)}{30} + \dfrac{-30x}{30} } = 10$

some simplification
$\displaystyle \dfrac{1}{\dfrac{0.25}{30}+\dfrac{0.375}{1.5(20)}+ \dfrac{2x}{2(15)}+ \dfrac{15}{30} + \dfrac{-30x}{30} } = 10$

more
$\displaystyle \dfrac{1}{\dfrac{0.25 + 0.375 + 2x + 15 - 30x}{30} } = 10$

etc
$\displaystyle \dfrac{1}{\dfrac{ 15.625 - 28x }{30} } = 10$

big step simplification

$\displaystyle \dfrac{30}{15.625 - 28x } = 10$

...
$\displaystyle 30 = 10 (15.625) - 280x$

...
$\displaystyle 156.25 - 30 = 280x$

to this

$\displaystyle 126.25 = 280x$

methodical systematic

.
• Sep 9th 2009, 10:11 AM
jello
You guys rock! Thank you so much for the speedy response and detailed steps.

When you turned

(1-(0.5+x)) into (0.5-x)

does that refer to a special rule? The 1 is meaningless? Why didn't 0.5 become negative as well as x?
• Sep 9th 2009, 10:13 AM
e^(i*pi)
Quote:

Originally Posted by jello
You guys rock! Thank you so much for the speedy response and detailed steps.

When you turned

(1-(0.5+x)) into (0.5-x)

does that refer to a special rule? The 1 is meaningless? Why didn't 0.5 become negative as well as x?

1-(0.5+x) = 1-0.5-x

As 1-0.5 = 0.5 that is why it's positive
• Sep 9th 2009, 11:49 AM
jello
AAAHHH dunce of the day for me!

Thanks again everyone.