a) \(\dfrac{x+5}{4}-\dfrac{x}{2}+1=0\)

<=> \(\dfrac{x+5-2x+4}{4}=0\)

<=> -x + 9 = 0 <=> x = 9

b) \(3\left(x+2\right)=\dfrac{x-4}{3}\)

<=> 9x + 18 = x-4

<=> 8x = -22

<=> x = \(\dfrac{-11}{4}\)

\(\left(x-1\right).3+3x\left(x-4\right)+1=0\)

\(\Rightarrow3x-3+3x^2-12x+1=0\)

\(\Rightarrow3x^2-9x-2=0\)

\(\Rightarrow3\left(x^2-\frac{2.3}{2}.x+\frac{9}{4}\right)-\frac{35}{4}=0\)

\(\Rightarrow3\left(x-\frac{3}{2}\right)^2=\frac{35}{4}\Rightarrow\left(x-\frac{3}{2}\right)^2=\frac{35}{12}\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{3}{2}=\sqrt{\frac{35}{12}}\\x-\frac{3}{2}=-\sqrt{\frac{35}{12}}\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=\sqrt{\frac{35}{12}}+\frac{3}{2}\\x=\frac{3}{2}-\sqrt{\frac{35}{12}}\end{cases}}\)

Vậy.....................

a,

\(x:\frac{3}{4}+\frac{1}{4}=-\frac{2}{3}\)

\(x:\frac{3}{4}=-\frac{2}{3}-\frac{1}{4}=-\frac{11}{12}\)

\(x=-\frac{11}{12}.\frac{3}{4}=-\frac{11}{16}\)

a)\(x:\frac{3}{4}+\frac{1}{4}=-\frac{2}{3}\)

\(x:\frac{3}{4}=-\frac{2}{3}-\frac{1}{4}\)

\(x:\frac{3}{4}=-\frac{11}{12}\)

\(x=-\frac{11}{16}\)

b)\(\frac{1}{3}x+\frac{2}{5}\left(x+1\right)=0\)

\(\frac{1}{3}x+\frac{2}{5}x+\frac{2}{5}=0\)

\(\left(\frac{1}{3}+\frac{2}{5}\right)x+\frac{2}{5}=0\)

\(\frac{11}{15}x=-\frac{2}{5}\)

\(x=-\frac{6}{11}\)

\(\left(x-\frac{1}{2}\right)\left(y+\frac{1}{3}\right)\left(z-2\right)=0\) và \(x+2=y+3=z+4\)

\(\Rightarrow x-\frac{1}{2}=0\) hoặc \(y+\frac{1}{3}=0\) hoặc \(z-2=0\)

\(\Rightarrow x=\frac{1}{2}\)            |         \(y=-\frac{1}{3}\)     |       \(z=2\)

Khi \(x=\frac{1}{2}\) thì:

\(\frac{1}{2}+2=\frac{5}{2}\)

\(y=\frac{5}{2}-3=-\frac{1}{2}\)

\(z=\frac{5}{2}-4=\frac{-3}{2}\)

Khi \(y=\frac{-1}{3}\)  thì:

\(\frac{-1}{3}+3=\frac{8}{3}\)

\(x=\frac{8}{3}-2=\frac{2}{3}\)

\(z=\frac{8}{3}-4=-\frac{4}{3}\)

Khi \(z=2\) thì:

\(2+4=6\)

\(x=6-2=4\)

\(y=6-3=3\)

Vậy (x,y,z) = \(\left(\frac{1}{2};-\frac{1}{2};-\frac{3}{2}\right)\)    ;    \(\left(\frac{2}{3};-\frac{1}{3};-\frac{4}{3}\right)\)  ;    \(\left(4;3;2\right)\)

Ta có: a) | x - 1,7 | = 2,3

     <=> x - 1,7 = 2,3

            x - 1,7 = -2,3

     <=> x = 2,3 + 1,7

            x = -2,3 + 1,7      

   <=>  x = 4

           x = -0,6

b) | x + 3/4 | -1/3 = 0

a) Th1 : \(x-1,7\ge0=>x\ge1,7\)

Pt trở thành :

  \(x-1,7=2,3\)

\(=>x=2,3+1,7=>x=4\) ( thỏa mãn )

Th2 : \(x-1,7< 0=>x< 1,7\)

PT trở thành :

 \(-x+1,7=2,3\)

\(=>-x=0,6\)

\(=>x=-0,6\)( thỏa mãn )

Vậy nghiệm của pt trên là : \(\orbr{\begin{cases}x=4\\x=-0,6\end{cases}}\)

b; \(\dfrac{1}{x}\) (\(x\) ≠ 0)

 \(\dfrac{1}{x}\) \(\in\) Z ⇔ 1 ⋮ \(x\) ⇒ \(x\) \(\in\) {-1; 1}

Vậy \(x\) \(\in\) {-1; 1}

a) \(\left(x+5\right)\left(x-4\right)=0\)

\(\Rightarrow\hept{\begin{cases}x=-5\\x=4\end{cases}}\)

b) \(\left(x-1\right)\left(x-3\right)=0\)

\(\Rightarrow\hept{\begin{cases}x=1\\x=3\end{cases}}\)

c) \(\left(3-x\right)\left(x-3\right)=0\Rightarrow x=3\)

d) \(x\left(x+1\right)=0\Rightarrow\hept{\begin{cases}x=0\\x=-1\end{cases}}\)

(x+5)(x-4) = 0

\(\orbr{\begin{cases}x+5=0\\x-4=0\end{cases}}\)

\(\orbr{\begin{cases}x=0-5\\x=0+4\end{cases}}\)

\(\orbr{\begin{cases}x=-5\\x=4\end{cases}}\)

a)\(\frac{1}{4}+\frac{1}{3}:2x=-5\)

   \(\frac{1}{3}:2x=-5-\frac{1}{4}\)

   \(\frac{1}{3}:2x=-\frac{21}{3}\)

   \(2x=\frac{1}{3}:\left(\frac{-21}{3}\right)\)

   \(2x=-\frac{1}{21}\)

   \(x=\frac{-1}{42}\)

b)\(\left(3x-\frac{1}{4}\right).\left(x+\frac{1}{2}\right)=0\)

\(\Rightarrow\left[\begin{array}{nghiempt}3x-\frac{1}{4}=0\\x+\frac{1}{2}=0\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}3x=\frac{1}{4}\\x=-\frac{1}{2}\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{1}{12}\\x=-\frac{1}{2}\end{array}\right.\)

c)\(\left(2x-5\right).\left(\frac{3}{2}x+9\right).\left(0,3x-12\right)=0\)

   \(\Rightarrow\left[\begin{array}{nghiempt}2x-5=0\\\frac{3}{2}x+9=0\\0,3x-12=0\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}2x=5\\\frac{3}{2}x=-9\\0,3x=12\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{5}{2}\\x=-6\\x=40\end{array}\right.\)

a) 1/4 + 1/3 : 2x = -5

=> 1/3 : 2x = -5 - 1/4

=> 1/3 : 2x = -21/4

=> 2x = 1/3 : (-21/4) = -4/63

=> x = -4/63 : 2 = -2/63