# Solve each equation for x a(3tx - 2b) = c(dx - 2)

Solve each equation for x $a\left(3tx-2b\right)=c\left(dx-2\right)$
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Yusuf Keller
Use the Distributive Property:
$a\left(3tx-2b\right)=3atx-2ab$
and
$c\left(dx-2\right)=cdx-2c$
So, the equation becomes
$3atx-2ab=cdx-2c$
We want the collect all terms with x on the left side, so subtract cdx from both sides:
$3atx-2ab-cdx=-2c$
We want to collect all terms with x on the right side, so add 2ab to both sides:
$3atx-cdx=2ab-2c$
Use the Distribute Property:
$3atx-cdx=\left(3at-cd\right)x$,
hence
$\left(3at-cd\right)x=2ab-2c$
Divide both sides by $3at-cd$ to obtain the solution:
$x=\frac{2ab-2c}{3at-cd}$
The denominators must not be 0. So, we have one restriction:
$3at-cd\ne 0$