# Thread: Struggling to simplyfy an equation :o(

1. ## Struggling to simplyfy an equation :o(

Hi, I have been trying to get my head around simplifying equations and was doing ok until I met this one:
(a+bx)/cx=d+5 Im trying to solve for x and it's cx thats my brick wall. Would someone be kind enough to guid me through it please.?

2. ## Re: Struggling to simplyfy an equation :o(

Originally Posted by nejuleho
Hi, I have been trying to get my head around simplifying equations and was doing ok until I met this one:
(a+bx)/cx=d+5 Im trying to solve for x and it's cx thats my brick wall. Would someone be kind enough to guid me through it please.?
\displaystyle \displaystyle \begin{align*} \frac{a + b\,x}{c\,x} &= d + 5 \\ a + b\,x &= c\,x\left(d + 5\right) \end{align*}

Now expand and then collect like terms

3. ## Re: Struggling to simplyfy an equation :o(

Thx for such a prompt reply! I did actually get this far it's the expansion that's flooring me, how can it expand to cxd +5cx ? what am I doing wrong ?

4. ## Re: Struggling to simplyfy an equation :o(

Originally Posted by nejuleho
Thx for such a prompt reply! I did actually get this far it's the expansion that's flooring me, how can it expand to cxd +5cx ? what am I doing wrong ?
That's exactly what you should get when you expand it, the term on the outside of the brackets is multiplied by every term inside the brackets.

5. ## Re: Struggling to simplyfy an equation :o(

Which gives a+bx = cxd +5cx , as I understand things there are no like terms to combine, I think I'm missing something...

6. ## Re: Struggling to simplyfy an equation :o(

Hello, nejuleho!

$\displaystyle \text{Solve for }x:\;\;\frac{a+bx}{cx} \:=\:d+5$

$\displaystyle \begin{array}{ccccc}\text{Multiply by }cx: & a+ bx \:=\:cx(d+5) \\ \\ \text{Expand:} & a+bx \:=\:cdx + 5cx \\ \\ \text{Subtract }bx: & a \:=\:cdx + 5cx - bx \\ \\ \text{Factor:} & a \:=\:(cd + 5c - b)x \\ \\ \text{Therefore:} & \dfrac{a}{cd+5c-b} \:=\:x \end{array}$

7. ## Re: Struggling to simplyfy an equation :o(

Ah! thank you both so much. I see my error now I did actually get as far as subtracting bx in one of my attempts but failed to factorize and apply the operator logic to complete.