1. 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!

2. Hello jello

Welcome to Math Help Forum!
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.)

3. 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

.

4. 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?

5. 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

6. AAAHHH dunce of the day for me!

Thanks again everyone.