# Equation Sorting

1. Jul 27, 2009

### frogtag

Can anyone help me rearrange this equation so that t is isolated please, it's driving me nuts.

x = tB + (1 - t)A

all I can seem to do so far is isolate one of the t's...

1...

x - (1-t)A = tB

2...

x - (1-t)A
---------- = t
B

2. Jul 27, 2009

### Kaimyn

Have a hint:
Expand the brackets...

If you are still stuck, show us what you have done so far.

3. Jul 27, 2009

### frogtag

If it is a homework question its about 16 years late! No it's just been a very long time since my A-levels and having 2 seperate t variables is throwing me. But I'll have a go and post my failure in a bit!

4. Jul 27, 2009

### frogtag

Okay ...

x = tB + (1-t)A

x - tB = (1-t)A or x - tB = A(1-t)

x - tB = 1A - tA

x - tB = A - tA

Not much so far...?

5. Jul 27, 2009

### Kaimyn

The key is to get everything with the variable you want onto one side, and everything else on the other.

How can you manipulate that equation to get the t's onto one side? How can you "fuse" the t's together? How can you get rid of the rest?

6. Jul 27, 2009

### frogtag

Quick clue ... is this going to be a quadratic?

7. Jul 27, 2009

### arildno

As Treebeard said: DON'T BE HASTY!

Do NOT move over the tB term as fast as you have done..

8. Jul 27, 2009

### Kaimyn

No, it won't be a quadratic... There are no exponents involved

9. Jul 27, 2009

### HallsofIvy

Staff Emeritus
Add tB to both sides then subtract A from both sides.

10. Jul 27, 2009

### frogtag

I have got that far already, used...

t = 0.5, A = 2.0 & B = 3.0 to prove it,

x = tB + (1-t)A
x = 0.5 x 3.0 + (1 - 0.5) x 2.0
x = 1.5 + (0.5) x 2.0
x = 1.5 + 1.0
x = 2.5

then expanded the brackets,

x = tB + 1A - tA
x = tB + A - tA
x = 0.5 x 3.0 + 2.0 - 0.5 x 2.0
x = 1.5 + 2.0 - 1.0
x = 2.5

then moved bits around,

x - A = tB - tA
2.5 - 2.0 = 0.5 x 3.0 - 0.5 x 2.0
0.5 = 1.5 - 1.0
0.5 = 0.5

maths all seems good, now just working on how to get t on own...

11. Jul 27, 2009

### frogtag

B - A
----- = x - A
t

(B - A) / t = x - A
(3.0-2.0) / 0.5 = 2.5 - 2.0
1.0 / 0.5 = 0.5
0.5 = 0.5

That works...

12. Jul 27, 2009

### frogtag

t = (B - A) / (x - A) ????

13. Jul 27, 2009

### Mentallic

$$x - tB = A - tA$$

look back at this step, and like has already been said, get all the parts with t onto one side, and all the other stuff on the other side. i.e. Add tB and subtract A from both sides (or equivalently, add tA and subtract x from both sides)

Now, use the rule of factoring. The factoring is the opposite to expanding (so, putting the variables back into brackets).

14. Jul 27, 2009

### Mentallic

You're close, but not quite right.

15. Jul 27, 2009

### HallsofIvy

Staff Emeritus
From x - A = tB - tA you have x- A= (B- A)t.

Since t is multiplied by B- A on the right side, you get t alone by doing the opposite of multiplying