Hello there!
We are given the equation:
[tex] \displaystyle \large{jr + se = jb + f}[/tex]
We are going to isolate j. First, subtract both sides by jb.
[tex] \displaystyle \large{jr + se - jb = jb - jb+ f} \\ \displaystyle \large{jr + se - jb = f}[/tex]
Then subtract both sides by se to leave only jr and jb.
[tex] \displaystyle \large{jr + se - jb - se= f - se} \\ \displaystyle \large{jr - jb = f - se}[/tex]
For jr-jb, we can common factor out the j-term.
[tex] \displaystyle \large{j(r - b)= f - se}[/tex]
For r-b, treat it as one term. Then we divide both sides by r-b.
[tex] \displaystyle \large{ \frac{j(r - b)}{r - b} = \frac{f - se}{r - b} } \\ \displaystyle \large{ j= \frac{f - se}{r - b} }[/tex]
Hence, j = f - se / r - b
Alternate Solution
This is an alternate solution. We can simplify the fractional expression by separating each terms.
[tex] \displaystyle \large{ j= \frac{f - se}{r - b} } \\ \displaystyle \large{ j= \frac{f}{r - b} + \frac{ - se}{r - b} }[/tex]
Since se is in negative, we replace + as - and cancel -se to se.
[tex] \displaystyle \large{ j= \frac{f - se}{r - b} } \\ \displaystyle \large{ j= \frac{f}{r - b} - \frac{ se}{r - b} }[/tex]
The simplifed answer is j = ( f / r - b ) - ( se / r - b l
These two answers work and are correct.
Let me know if you have any questions!
Topic: Literal Equation (Factorization Involved)
