Help solve, I got quiz tomorow on this stuff need quick help!

**elitescouter** · July 8th 2009, 10:10 PM

Allright so tomorow I got a quiz on this stuff. I just need someone to show me step by step how to do this!

$ \frac{bx}{a}+\frac{1}{5}=2x$ SOLVE FOR X

$ \frac{3}{M}=\frac{M}{5}$ SOLVE FOR M

$ \frac{1}{U}=\frac{y}{k}+\frac{1}{h}$ SOLVE FOR K

$ \frac{V-6}{5}+\frac{V-8}{15}+\frac{V}{10}=0$ SOLVE FOR V

$ \frac{5}{w+3}+4=15$ SOLVE FOR w

and some similar problems that I need to isolate

$ \frac{K}{M}=P+\frac{a}{M^2}$ ISOLATE a

Thanks!!!

**Stroodle** · July 8th 2009, 10:29 PM

$\frac{bx}{a}+\frac{1}{5}=2x$

First establish a common denominator:

$\frac{5bx}{5a}+\frac{a}{5a}=\frac{10ax}{5a}$

Then solve for $x$

$10ax-5bx=a$

$x(10a-5b)=a$

$x=\frac{a}{10a-5b}$

$x=\frac{a}{5(2a-b)}$

Use the same process for this one:

$\frac{1}{U}=\frac{y}{k}+\frac{1}{h}$

$\frac{hk}{hkU}=\frac{hUy}{hkU}+\frac{kU}{hkU}$

$hk-kU=hUy$

$k(h-U)=hUy$

$\therefore k=\frac{hUy}{h-U}$

Can you now use this process to do the other ones? Each term just needs to have the same denominator.

For the last question:

$\frac{K}{M}=P+\frac{a}{M^2}$

$\frac{a}{M^2}=\frac{K}{M}-P$

$a=M^2(\frac{K}{M}-P)$

$a=\frac{KM^2}{M}-PM^2$

$a=KM-PM^2$

$a=M(K-PM)$

**Stroodle** · July 8th 2009, 11:00 PM

$\frac{5}{w+3}+4=15$

For this question you can multiply each term by $(w+3)$ to get rid of the fraction.

$5+4(w+3)=15(w+3)$

$4w+17=15w+45$

$11w=-28$

$\therefore w=-\frac{28}{11}$

**elitescouter** · July 8th 2009, 11:35 PM

Sorry to bother u but u think u can help me with

$<html> <head> <style type=$ img.top {vertical-align:15%;} $ \frac{3}{M}=\frac{M}{5}$ SOLVE FOR M" alt=" $ \frac{3}{M}=\frac{M}{5}$ SOLVE FOR M" />

I get stuck half way through it.

**yeongil** · July 8th 2009, 11:45 PM

Originally Posted by elitescouter

Sorry to bother u but u think u can help me with

$\frac{3}{M}=\frac{M}{5}$ SOLVE FOR M

I get stuck half way through it.

Just cross multiply:
$\begin{aligned} \frac{3}{M} &= \frac{M}{5} \\ M^2 &= 15 \end{aligned}$

Now find M.

01

**arze** · July 8th 2009, 11:46 PM

Originally Posted by elitescouter

Sorry to bother u but u think u can help me with

$<html> <head> <style type=$ img.top {vertical-align:15%;} $ \frac{3}{M}=\frac{M}{5}$ SOLVE FOR M" alt=" $ \frac{3}{M}=\frac{M}{5}$ SOLVE FOR M" />

I get stuck half way through it.

make every term have the same denominator.
M^2=3*5
M=sqrt (15)

**Stroodle** · July 8th 2009, 11:50 PM

Don't forget the $\pm$

$m^2=15$

$\therefore m=\pm \sqrt{15}$

**arze** · July 8th 2009, 11:51 PM

oops forgot that!

**allyourbass2212** · July 9th 2009, 06:45 AM

Originally Posted by yeongil

Just cross multiply:
$\begin{aligned} \frac{3}{M} &= \frac{M}{5} \\ M^2 &= 15 \end{aligned}$

Now find M.

01

What other alternatives other than cross multiplying are possible here? Because if it were me I would multiply by the reciprocal $\frac{m}{3}*\frac{3}{m}=\frac{m}{5}*\frac{m}{3}$ . Which would equal $\frac{m^2}{15}$

**Stroodle** · July 9th 2009, 07:16 AM

You can use a common denominator:

$\frac{3}{M}=\frac{M}{5}$

$\frac{15}{5M}=\frac{M^2}{5M}$

$M^2=15$

$\therefore M=\pm\sqrt{15}$

**Prove It** · July 9th 2009, 07:21 AM

Originally Posted by allyourbass2212

What other alternatives other than cross multiplying are possible here? Because if it were me I would multiply by the reciprocal $\frac{m}{3}*\frac{3}{m}=\frac{m}{5}*\frac{m}{3}$ . Which would equal $\frac{m^2}{15}$

Your method would be fine as long as you keep your eye on BOTH sides of the equation.

$\frac{3}{M} = \frac{M}{5}$

$\frac{3}{M}\cdot\frac{M}{3} = \frac{M}{5}\cdot\frac{M}{3}$

$1 = \frac{M^2}{15}$

$15 = M^2$

$\pm\sqrt{15} = M$ .

**Prove It** · July 9th 2009, 07:23 AM

Originally Posted by Stroodle

$\frac{5}{w+3}+4=15$

For this question you can multiply each term by $(w+3)$ to get rid of the fraction.

$5+4(w+3)=15(w+3)$

$4w+17=15w+45$

$11w=-28$

$\therefore w=-\frac{28}{11}$

It's easier if you subtract 4 from both sides first...

$\frac{5}{w + 3} + 4 = 15$

$\frac{5}{w + 3} = 11$

$\frac{w + 3}{5} = \frac{1}{11}$

$w + 3 = \frac{5}{11}$

$w = \frac{5}{11} - 3$

$w = -\frac{28}{11}$ .

**allyourbass2212** · July 9th 2009, 07:46 AM

Embarrassingly enough the basic algebra book I am reading through does not cover how to solve when the equation looks as such.

$1 = \frac{M^2}{15}$

$15 = M^2$

Would you please explain the steps involved in how $1 = \frac{M^2}{15}$ equals $15 = M^2$
?

Many thanks

**Prove It** · July 9th 2009, 07:50 AM

Originally Posted by allyourbass2212

Embarrassingly enough the basic algebra book I am reading through does not cover how to solve when the equation looks as such.

$1 = \frac{M^2}{15}$

$15 = M^2$

Would you please explain the steps involved in how $1 = \frac{M^2}{15}$ equals $15 = M^2$
?

Many thanks

Can you see that $M^2$ is divided by 15?

To undo this, we have to multiply both sides by 15.

So $1 = \frac{M^2}{15}$

$1\cdot 15 = \frac{M^2}{15}\cdot 15$

$15 = M^2$

Then to undo the squaring, we have to take the square root of both sides.

So $\pm \sqrt{15} = M$ .

**allyourbass2212** · July 9th 2009, 07:51 AM

Ah yes very good thank you.

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