# Thread: unsure on the next step?

1. ## unsure on the next step?

Rearrange the following equation to find x in terms of a and b in simplest form (assume that a =/-3b)

the / should be through the = to show a is not equal to -3b

Couldnot find the key for it sorry!

3b(x+3b)=a(a-x)

3bx+9b^2=a^2-ax

(3b-a)x=a^2-9b^2

(3b-a)x=(a-3b)(a+3b)

this is where i get unsure.

I think then it becomes

(a-3b)(a+3b)
- ______________

3b-a

which then becomes

x= -(a+b)

which is x= a-b

Are my workings out right or am I completley of the mark?

Apologies for the way i may have presented my workings out still getting to grips with showing my workings out on a computer

2. ## Re: unsure on the next step?

$\displaystyle 3b(x+3b)=a(a-x)$

$\displaystyle 3bx+9b^2=a^2-ax$

$\displaystyle 3bx+ax+9b^2=a^2+ax-ax=a^2$

Subtract "9b^2" from both sides

$\displaystyle x(3b+a)+9b^2-9b^2=a^2-9b^2$

$\displaystyle (3b+a)x=(a-3b)(a+3b)$

Now divide both sides by (3b+a) to get the expression for "x"

$\displaystyle \frac{(3b+a)x}{(3b+a)}=\frac{(a-3b)(a+3b)}{(3b+a)}$

and simplify the last line.

As the denominator cannot be zero,
the given condition is

$\displaystyle a\ne\ -3b$

3. ## Re: unsure on the next step?

so would i be correct in saying x =(a-3b) so x =-a+3b

4. ## Re: unsure on the next step?

Originally Posted by Orlando
so would i be correct in saying x =(a-3b) so x =-a+3b
$\displaystyle x =(a-3b)$ does not imply $\displaystyle x =-a+3b$

5. ## Re: unsure on the next step?

Originally Posted by Orlando
so would i be correct in saying x =(a-3b) so x =-a+3b