# solving this linear equation

• Nov 11th 2008, 08:31 AM
Larianne
solving this linear equation
Solve for x in terms of a and b

2a + 3(x-2) = ax + b
---
3

^^( that's 2a over 3)

I know it's probably simple but I can't get it!
• Nov 11th 2008, 08:57 AM
masters
Quote:

Originally Posted by Larianne
Solve for x in terms of a and b

2a + 3(x-2) = ax + b
---
3

^^( that's 2a over 3)

I know it's probably simple but I can't get it!

Hi Larianne,

It's only simple for those who already know how to do it.

$\displaystyle \frac{2a}{3}+3(x-2)=ax+b$

$\displaystyle \frac{2a}{3}+3x-6=ax+b$

Multiply through by 3.

$\displaystyle 2a+9x-18=3ax+3b$

Group x terms together.

$\displaystyle 9x-3ax=3b-2a+18$

Factor out a 3x on the left.

$\displaystyle 3x(3-a)=3b-2a+18$

Divide both sides by 3(3-a).

$\displaystyle x=\frac{3b-2a+18}{3(3-a)}$
• Nov 11th 2008, 09:02 AM
Larianne
Thank Masters!

So I can't get x as a 'whole' number? That's what I was having trouble with.

Larianne.
• Nov 11th 2008, 09:27 AM
masters
Quote:

Originally Posted by Larianne
Thank Masters!

So I can't get x as a 'whole' number? That's what I was having trouble with.

Larianne.

You're dealing with 'literals' here. This means your answer will not be a number. Both a and b are unknown variables at this time, so we just solve for whichever variable is required. It's like converting formulas like this:

$\displaystyle d=rt$ Distance = rate X time

$\displaystyle r=\frac{d}{t}$ Rate = distance divided by time

$\displaystyle t=\frac{d}{r}$ Time = distance divided by rate.