1)9/14х+18=-2/3х+17; 2)-8/15х-11=4/9х+11.

1) [latex]\frac{9}{14}x + 18 = -\frac{2}{3}x + 17\\ \frac{9}{14}x + \frac{2}{3}x = 17 - 18\\ \frac{9*3+2*14}{14*3}x = -1\\ 55x = -1*42\\ x = -\frac{42}{55}\\ [/latex]  2) [latex]-\frac{8}{15}x-11=\frac{4}{9}x+11\\ -\frac{8}{15}x-\frac{4}{9}x=11+11\\ -\frac{8*3+4*5}{45}x=22\\ -\frac{44}{45}x=22\\ -44x=22*45\\ x=-\frac{22*45}{44}\\ x=-\frac{45}{2}=-22\frac{1}{2}\\[/latex]