Question

При всех значениях параметра а решите уравнение
1)3ax-2x+1,5a=3x+7
2)3(a-5)x=8-1,1a

Answer 1

$1) 3ax-2x+1,5a=3x+7 \ 3ax+1,5a=5x+7 \ 1,5a(2x+1)=5x+7 \ frac{3}{2}a=frac{5x+7}{2x+1} \ a=frac{2(5x+7)}{3(2x+1)} \ (1) a=0, \ 5x+7=0 \ 5x=-7 \ x=-frac{7}{5} \ (2) a<0, \ frac{2*5(x+frac{7}{5})}{3*2(x+frac{1}{2})}<0 \ x in (-frac{7}{5};-frac{1}{2}) \ (3) a>0, \ frac{2*5(x+frac{7}{5})}{3*2(x+frac{1}{2})}>0 \ x in (-infty ; -frac{7}{5}) cup (-frac{1}{2};+infty ) \ \ \ 2) 3(a-5)x=8-1,1a \ 3ax-15x=8-1,1a \ 3ax+1,1a=15x+8 \ a(3x+1,1)=15x+8 \ a=frac{15x+8}{3x+1,1} \ (1) a=0, \ 15x+8=0 \ 15x=-8 \ x=-frac{8}{15} \ (2) a<0, \ frac{15(x+frac{8}{15})}{3(x+frac{11}{30})}<0 \ x in (-frac{8}{15};-frac{11}{30}) \ (3) a>0, \ frac{15(x+frac{8}{15})}{3(x+frac{11}{30})}>0 \ x in (-infty; -frac{8}{15}) cup (-frac{11}{30};+infty)$