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{ (j(r - b))/(r - b) = (f - se)/(r - b) } \\ \displaystyle \large{ j= (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= (f - se)/(r - b) } \\ \displaystyle \large{ j= (f)/(r - b) + ( - se)/(r - b) }`

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

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