# Math Help - Changing the subject of a formula

1. ## Changing the subject of a formula

How do I make 'x' the subject for these? Can you please show all the steps and working out:

1) h = d - b/x
2) r - m/x = e^2
3) t^2 = b - n/x

4) 3M = M + N/P+x
5) m^2/x - n = -p
6) t = w - q/x

Thanks if you can help!

2. Originally Posted by Lalis
How do I make 'x' the subject for these? Can you please show all the steps and working out:

1) h = d - b/x
$h= d-\frac{b}{x}$

$h-d= -\frac{b}{x}$

$d-h= \frac{b}{x}$

$x(d-h)= b$

$x= \frac{b}{d-h}$

Now you have a go.

3. Thanks. But the others are hard as well

I'll give it a go and if I can't I'll come back.

4. Originally Posted by pickslides

$h-d= -\frac{b}{x}$

$d-h= \frac{b}{x}$
I didn't get this bit. Could you explain please?

5. I multiplied -1 through both sides.

Here's a bit more detail

$h-d= -\frac{b}{x}$

$-1 \times (h-d)= -1 \times-\frac{b}{x}$

$-h+d=\frac{b}{x}$

Then swapping the order on the LHS

$d-h=\frac{b}{x}$

6. Hi sorry to bother you again, but I used the other one as an example and did #2. Can you check it?

r - m/x = e^2
-m/x = e^2 - r
m/x = r - e^2
m = x(r - e^2)
m/r - e^2 = x

And also I have two questions. Why did you multiply both sides by -1, and what is the purpose of swapping th order on the LHS? Thanks so much!

7. Originally Posted by Lalis
Hi sorry to bother you again, but I used the other one as an example and did #2. Can you check it?

r - m/x = e^2
-m/x = e^2 - r
m/x = r - e^2
m = x(r - e^2)
m/r - e^2 = x
This is correct, be careful though, use brackets.

m/(r - e^2) = x

Originally Posted by Lalis
And also I have two questions. Why did you multiply both sides by -1, and what is the purpose of swapping th order on the LHS? Thanks so much!
-1 on both sides gets rid of any negative values.

Swapping the order makes it all neater.

8. You wrote m/r- e^2= x and Pickslides wrote "be careful, though, use brackets m/(r- e^2)= x".

Which makes me ask- is your original problem r- m/x= e^2 (which is $r- \frac{m}{x}= e^2$) or (r- m)/x= e^2 (which is $\frac{r- m}{x}= e^2$)? Those are very different equations with very different solutions.

Similarly, was your first problem h= d- b/x ( $h= d- \frac{b}{x}$) or h= (d- b)/x ( $h= \frac{d- b}{x}$?

pickslides assumed it was the first in both of those.