# Thread: Need help Transforming Formulas

1. ## Need help Transforming Formulas

S= a-rl ; l
l-r

Also, is this correct?

l= a+(n-l)d ; n

= l-a+1 = n

I'm struggling a bit on this lesson

Thanks

2. Originally Posted by chris678
S= a-rl ; l
l-r

Also, is this correct?

l= a+(n-l)d ; n

= l-a+1 = n

I'm struggling a bit on this lesson

Thanks
Hi Chris678,

Some students have trouble solving literal equations. Just remember, the rules are the same as solving equations in one variable. It's just that nothing goes away in literal equations. They just move around.

Solve the following for l.

$\displaystyle S=\frac{a-rl}{l-r}$

First, multiply both sides by $\displaystyle (l - r)$. The distribute the S.

$\displaystyle S(l-r)=a-rl$

$\displaystyle Sl-Sr=a-rl$

Transpose $\displaystyle -rl$ to the left side and $\displaystyle -Sr$ to the right side.

$\displaystyle Sl+rl=Sr+a$

Factor $\displaystyle l$ from the left side.

$\displaystyle l(S+r)=Sr+a$

Finally, divide both sides by $\displaystyle S + r$.

$\displaystyle \boxed{l=\frac{Sr+a}{S+r}}$

In your second one you are solving for $\displaystyle n$.

$\displaystyle l=a+(n-1)d$

Distribute the $\displaystyle d$ on the right side.

$\displaystyle l=a+dn-d$

Next, transpose the $\displaystyle a$ and $\displaystyle -d$ to the left side.

$\displaystyle l-a+d=dn$

Finally, divide both sides by $\displaystyle d$.

$\displaystyle \boxed{\frac{l-a+d}{d}=n}$