Question

Solve the equation for j
jr+se=jb+f

Answer 1

Hello there!

We are given the equation:

$\displaystyle \large{jr + se = jb + f}$

We are going to isolate j. First, subtract both sides by jb.

$\displaystyle \large{jr + se - jb = jb - jb+ f} \\ \displaystyle \large{jr + se - jb = f}$

Then subtract both sides by se to leave only jr and jb.

$\displaystyle \large{jr + se - jb - se= f - se} \\ \displaystyle \large{jr - jb = f - se}$

For jr-jb, we can common factor out the j-term.

$\displaystyle \large{j(r - b)= f - se}$

For r-b, treat it as one term. Then we divide both sides by r-b.

$\displaystyle \large{ \frac{j(r - b)}{r - b} = \frac{f - se}{r - b} } \\ \displaystyle \large{ j= \frac{f - se}{r - b} }$

Hence, j = f - se / r - b

Alternate Solution

This is an alternate solution. We can simplify the fractional expression by separating each terms.

$\displaystyle \large{ j= \frac{f - se}{r - b} } \\ \displaystyle \large{ j= \frac{f}{r - b} + \frac{ - se}{r - b} }$

Since se is in negative, we replace + as - and cancel -se to se.

$\displaystyle \large{ j= \frac{f - se}{r - b} } \\ \displaystyle \large{ j= \frac{f}{r - b} - \frac{ se}{r - b} }$

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)