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.

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