Solve for x in terms of a and b
2a + 3(x-2) = ax + b
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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).
$\displaystyle x=\frac{3b-2a+18}{3(3-a)}$
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.