Rearranging Formula, making x the subject

[Guest]

Hi, we were rearranging formula to make [tex]x[/tex] 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 [tex]x[/tex] the subject we're told to "do the opposite" to achieve this.

The equation with our working:

[tex]y=5(x+3)[/tex]

[tex]\frac{y}{5}=x+3[/tex]

[tex]\frac{y}{5}-3=x[/tex]

Replacing [tex]x[/tex] with 2 as an example to test our result:

[tex]y=5(2+3)[/tex] (or) [tex]y=5[/tex]x[tex]5[/tex] (or) [tex]y=25[/tex]

[tex]\frac{25}{5}=5[/tex], [tex]-3=2[/tex], [tex]x=2[/tex]

[Guest]

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.
[tex]\frac{y}{5} = \frac{5(x + 3)}{5}[/tex]

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

[tex]\frac{y}{5} - 3 = x + 3 - 3[/tex]

[tex]\frac{y}{5} - 3 = x[/tex]

[Guest]

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

[Guest]

(OT) Thanks for confirming!