# How to Manipulate Relationships

Let's take a look at an example. We are given the following equation and need to solve for $a$.

$$4a = (10-2a)3$$

To start, we need to expand the right hand side, i.e. $3 \times (10-2a)$

$$4a = 30 -6a$$

Now we need to group the like terms together and isolate it on one side. In this case, we can move $6a$ to the left but remember whatever you do to one side you must do to the other. That is, since we need to add $6a$ to the right, we need to add $6a$ to the left. The new equation will look like this:

$$10a = 30$$

Now we need to isolate $a$ – we can do this by dividing both sides by the $a$'s coefficient (opposite of multiplying $10 \times a$)

$$\frac{10a}{10} = \frac{30}{10}$$

Therefore, $a = 3$

There is a video on the next page that demonstrates how to answer a typical manipulating relationship question you may come across in chemistry and also some sample questions.