2/3(-4/3x+1)=-4x-278/45

$$\\\frac{2}{3}(\frac{-4x}{3}+1)=-4x-\frac{278}{45}\\\\
\mbox{none of these fractions can be simplified so mult both sides by 45}\\\\
45\left( \frac{2}{3}(\frac{-4x}{3}+1)\right)=45\left(-4x-\frac{278}{45}\right) \\\\
15\left( 2(\frac{-4x}{3}+1)\right)=45\left(-4x-\frac{278}{45}\right) \\\\
30(\frac{-4x}{3}+1)=45*(-4x)-45*\frac{278}{45} \\\\
30*\frac{-4x}{3}+30*1=45*(-4x)-45*\frac{278}{45} \\\\
10*-4x+30=-180x-278 \\\\$$

You should be able to finish it from there.    

First, you can multiply both sides by 3 to get rid of potential fractions.

From there, you have to do basic algebra.

Sorry aziz but that will not get rid of the fractions - not even the algebraic fractions.  

Oh, I see...rats :p -- fractions are crazy!