Need help with Linear equations with unknown coefficients

Question

—cz+6z=tz+83 solving for z

Answer 1

Hi Sandra,

The first thing you want to do is to transform the original equation of -cz+6z=tz+83 to isolate the variable you want to solve for on one side, in this case "z". Using various things you learned in Algebra: First step: subtract tz from both sides yields:-cz-tz+6z=83 Next step factor out the z on the left to try to simplify it yields:z(-c-t+6)=83 Now we can isolate z by dividing each side by the coefficient of z, which yields: 83 / (-c -t +6)

Note: It doesn't really matter what order you put the 3 values in the denominator of 83, some people have preferences regarding where negative signs should be, but it doesn't change the answer. The answer to this problem isn't pretty, but I hope the explanation is helpful.

Good Luck in your class, Marla G.

Answer 2

Hello Sandra,

— cz + 6z = tz + 83

→ 6z - cz - tz = 83

→ (6 - c - t)z = 83

→ z = 83 / (6 - c - t)

I hope the above helps.

Thank you for posting the question, and have a great day!

Michael E.