# Rearranging Formula, making x the subject

### Rearranging Formula, making x the subject

Hi, we were rearranging formula to make $$x$$ the subject and for one equation our answer was different to our lecturers, but they failed to explain why they were right and we were wrong- if someone could that would be great.
When making $$x$$ the subject we're told to "do the opposite" to achieve this.

The equation with our working:

$$y=5(x+3)$$

$$\frac{y}{5}=x+3$$

$$\frac{y}{5}-3=x$$

Replacing $$x$$ with 2 as an example to test our result:

$$y=5(2+3)$$ (or) $$y=5$$x$$5$$ (or) $$y=25$$

$$\frac{25}{5}=5$$, $$-3=2$$, $$x=2$$
Guest

### Re: Rearranging Formula, making x the subject

You are right!
Here is the explanation:

1. You divide the both sides by 5
and since the both sides are equal the result is equal too.
$$\frac{y}{5} = \frac{5(x + 3)}{5}$$

$$\frac{y}{5} = (x + 3)$$
2. You subtract the both sides by -3

$$\frac{y}{5} - 3 = x + 3 - 3$$

$$\frac{y}{5} - 3 = x$$
Guest

### Re: Rearranging Formula, making x the subject

Note: I wanted to write
2. You subtract the both sides by 3 (not by -3)
Guest

### Re: Rearranging Formula, making x the subject

(OT) Thanks for confirming!
Guest