Start with
[tex]-\dfrac{1}{9}(x-27)+\dfrac{1}{3}(x+3)=x-17[/tex]
Distribute the multiplication:
[tex]-\dfrac{1}{9}x+3+\dfrac{1}{3}x+1=x-17[/tex]
Move all terms involving x to the left and all numbers to the right:
[tex]-\dfrac{1}{9}x+\dfrac{1}{3}x-x=-3-1-17[/tex]
Sum terms on both sides:
[tex]-\dfrac{7}{9}x=-21[/tex]
Divide both sides by -7/9 (i.e. multiply both sides by -9/7):
[tex]x=-21\left(-\dfrac{9}{7}\right) = 27[/tex]
