Question

Rezolvării in Q ecuatiile: 2×+1 pe 3 =0, (6)
B) 3×+0,5= -0,25
C)0,1x × -0.25=-0.34
D)(×-1): 3 pe 4= - 1 pe 6
E) 1 2 pe 1 -x= 5 pe 14.
F) 1 1 pe 3 x × - 0, (4) = ( - 2 pe 3 ) totul la puterea 2

Answer 1

    
[tex] \displaystyle a) \\ \frac{ 2x +1}{3}=0,(6) \\ \\ \frac{ 2x +1}{3}= \frac{6}{9} \\ \\ \frac{ 2x }{3} +\frac{ 1}{3} = \frac{2}{3} ~~~~~| * 3 \\ \\ 2x+1=2 \\ 2x=2-1 \\ \\ x= \frac{2-1}{2}=\boxed{\frac{1}{2}} [/tex]

$\displaystyle b) \\ 3x+0,5= -0,25 \\ 3x+ \frac{1}{2} = - \frac{1}{4} \\ \\ 3x = - \frac{1}{4}-\frac{1}{2} \\ \\ 3x = - \frac{3}{4} \\ \\ x = - \frac{3}{4} :3 = \boxed{-\frac{1}{4}}$

[tex]\displaystyle c) \\ 0,1x \cdot (-0,25)=-0,34 \\ \frac{1}{10}x \cdot \frac{-1}{4}=- \frac{34}{100} \\ \\ -\frac{1}{40}x= - \frac{17}{50} ~~~~~|*(- \frac{1}{10} ) \\ \\ \frac{1}{4}x= \frac{17}{5} \\ \\ x=\frac{17}{5}:\frac{1}{4}=\frac{17}{5}*\frac{4}{1}=\frac{17*4}{5*1}=\boxed{\frac{68}{5}}[/tex]

[tex]\displaystyle d) \\ (x-1): \frac{3}{4} = -\frac{1}{6} \\ \\ (x-1)=-\frac{1}{6} *\frac{3}{4} \\ x-1=-\frac{1*3}{6*4} \\ \\ x-1=-\frac{1}{2*4} \\ \\ x-1=-\frac{1}{8} \\ \\ x=-\frac{1}{8}+1=-\frac{1}{8}+ \frac{8}{8} =\frac{-1+8}{8}=\boxed{\frac{7}{8}}[/tex]

[tex]\displaystyle e) \\ \frac{12}{1 -x}= \frac{5}{14} \\ \\ 12*14 = 5(1-x) \\ 168=5-5x \\ 5x=5-168 \\ 5x=-163 \\ \\ x = \frac{-163}{5} =\boxed{-\frac{163}{5} }[/tex]

[tex]\displaystyle f) \\ \frac{11}{3} x *( - 0, (4) )= \left ( \frac{-2}{3} \right)^2 \\ \\ \frac{11}{3} x * \left( - \frac{4}{9} \right)= \left ( \frac{4}{9} \right) \\ \\ \frac{11}{3} x =\left ( \frac{4}{9} \right):\left( - \frac{4}{9} \right) \\ \\ \frac{11}{3} x =\left ( \frac{4}{9} \right) * \left( - \frac{9}{4} \right) \\ \\ \frac{11}{3} x = -\frac{4*9}{9*4} \\ \\ \frac{11}{3} x =-1 ~~~~~~~=\ \textgreater \ ~~x=-1*\frac{3}{11}=\boxed{-\frac{3}{11}}[/tex]