# Solving Literal Linear Equations

I am studying now for a Math methods SAC after the holidays. The teacher has given the class some revision questions and I have come across one question, which I don't have a proper way to approach. The text book doesn't explain much about these questions and does not provide any examples for me to follow.

So here is one of the questions.

Solve each of the following by making $m$ the subject.

$$d = 4x + m$$

If someone could explain how one should approach these types of questions it would be a great help. I don't need the answer to the question for me (I would prefer that you don't answer it), just how I would start to answer it and what is involved.

• What happens if you subtract the same amount from two amounts that are equal? – Fabio Somenzi Apr 2 '17 at 1:23
• "Solve each of the following by making $m$ the subject..." What does it mean by "solve"? If it is simply asking you to find an expression for $m$ in terms of the other variables, then do whatever you can to isolate $m$ alone on one side, in this example by subtracting $4x$ from each side, you arrive at $m=d-4x$. If you are given a system of equations, then perhaps more can be done using gaussian elimination, but as it stands, the usual meaning of "solve" as in find a point or a set of points which satisfies the equation, there is no cleaner answer than the original form given. – JMoravitz Apr 2 '17 at 1:23
• Thank you, @JMoravitz for your detailed comment. I have done the next question, which was 2m - x = 5e . This is my working. 2m = 5e + x, m = (5e + x) / 2. Is this the right way I should be working this out? – Chet Power Apr 2 '17 at 2:26
• Assuming that is the correct interpretation of the question, yes. – JMoravitz Apr 2 '17 at 2:30

## 1 Answer

What you want to do here is isolate $m$ on one side.

Have you tried subtracting $4x$ on both sides? $$d\color{red}{-4x}=4x+m\color{red}{-4x}$$