chiu thoi

\(\left(\frac{2}{11\times13}+\frac{2}{13\times15}+\frac{2}{15\times17}+\frac{2}{17\times19}+\frac{2}{19\times21}\right)\times462-x=19\)

\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)\times462-x=19\)

\(\left(\frac{1}{11}-\frac{1}{21}\right)\times462-x=19\)

\(\frac{10}{231}\times462-x=19\)

\(20-x=19\)

\(\Rightarrow x=20-19=1\)

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\(\frac{x-241}{17}+\frac{x-220}{19}+\frac{x-195}{21}+\frac{x-166}{23}=10\)

\(\Leftrightarrow\left(\frac{x-241}{17}-1\right)+\left(\frac{x-220}{19}-2\right)+\left(\frac{x-195}{21}-3\right)+\left(\frac{x-166}{23}-4\right)=0\)

\(\Leftrightarrow\frac{x-258}{17}+\frac{x-258}{19}+\frac{x-258}{21}+\frac{x-258}{23}=0\)

\(\Leftrightarrow\left(x-258\right)\left(\frac{1}{17}+\frac{1}{19}+\frac{1}{21}+\frac{1}{23}\right)=0\)

\(\Leftrightarrow x-258=0\)(vì \(\frac{1}{17}+\frac{1}{19}+\frac{1}{21}+\frac{1}{23}\ne0\))

\(\Leftrightarrow x=258\)

vậy phương trình có tập nghiệm là: S={258}

=> \(\frac{x-241}{17}-1+\frac{x-220}{19}-2+\frac{x-195}{21}-3+\frac{x-170}{22}-4=0\)

<=> \(\left(\frac{x-241}{17}-\frac{17}{17}\right)+\left(\frac{x-220}{19}-\frac{38}{19}\right)+\left(\frac{x-195}{21}-\frac{63}{21}\right)+\left(\frac{x-170}{22}-\frac{88}{22}\right)=0\)

<=> \(\frac{x-258}{17}+\frac{x-258}{19}+\frac{x-258}{21}+\frac{x-258}{22}=0\)

<=> \(\left(x-258\right).\left(\frac{1}{17}+\frac{1}{19}+\frac{1}{21}+\frac{1}{22}\right)=0\)

<=> x - 258 = 0  do \(\left(\frac{1}{17}+\frac{1}{19}+\frac{1}{21}+\frac{1}{22}\right)\ne0\)

=> x = 258

10=1+2+3+4

X=241+17x1=258

X=220+19x2=258

X=195+21x3=258

X=170+22x4=258.

a) x+26=39+(-5)=34

    x=34-26=8

b) IxI+50=(-I-26I)+76=(-26)+76=50

    IxI=50-50=0

=> x=0

c) IxI+17=(-21)+19=-2

    IxI=(-2)-17=-19

=> x thuộc tập hợp rỗng

a, x + 26 = 39 + (-5)

   x + 26 = 39 - 5

   x + 26 = 34

   x        = 34 - 26

   x        = 8

b, |x| + 50 = (-|-26|) +76

    |x| +50 = (-26) +76

    |x| +50 = 76 - 26

    |x| +50 = 50

    |x|        = 50 -50

    |x|        = 0

c, |x| + 17 = (-21)+19

    |x| + 17 = - (21-19)

    |x| + 17 = - 2

    |x| không tồn tại

d. |x-21|= 2.(|-11| + |-3|)

    |x-21|= 2.(11+3)

    |x-21|= 2.14

    |x-21|= 28

     x     = 28+21 hoặc 21-28

     x     = 49      hoặc -7

e. hình như lộn đề vì |x-54|-7|

\(\dfrac{x-241}{17}+\dfrac{x-220}{19}+\dfrac{x-195}{21}+\dfrac{x-166}{23}=10\)

\(\Leftrightarrow\dfrac{x-241}{17}+\dfrac{x-220}{19}+\dfrac{x-195}{21}+\dfrac{x-166}{23}-10=0\)

\(\Leftrightarrow(\dfrac{x-241}{17}-1)+(\dfrac{x-220}{19}-2)+(\dfrac{x-195}{21}-3)+(\dfrac{x-166}{23}-4)=0\)

\(\Leftrightarrow\dfrac{x-258}{17}+\dfrac{x-258}{19}+\dfrac{x-258}{21}+\dfrac{x-258}{23}=0\)

\(\Leftrightarrow\left(x-258\right)\left(\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{21}+\dfrac{1}{23}\right)=0\)

\(Do\) \(\left(\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{21}+\dfrac{1}{23}\right)\ne0\) \(nên\) \(để\) \(gt=0\)

\(\Leftrightarrow x-258=0\)

\(\Leftrightarrow x=258\)

\(Vậy...\)

d: ĐKXĐ: x<>-4; x<>-5; x<>-6; x<>-7

\(PT\Leftrightarrow\dfrac{1}{x+4}-\dfrac{1}{x+5}+\dfrac{1}{x+5}-\dfrac{1}{x+6}+\dfrac{1}{x+6}-\dfrac{1}{x+7}=\dfrac{1}{18}\)

=>\(\dfrac{1}{x+4}-\dfrac{1}{x+7}=\dfrac{1}{18}\)

=>\(\dfrac{x+7-x-4}{\left(x+4\right)\left(x+7\right)}=\dfrac{1}{18}\)

=>x^2+11x+28=54

=>x^2+11x-26=0

=>(x+13)(x-2)=0

=>x=2 hoặc x=-13

e: \(\dfrac{x-241}{17}+\dfrac{x-220}{19}+\dfrac{x-195}{21}+\dfrac{x-166}{23}=10\)

\(\Leftrightarrow\left(\dfrac{x-241}{17}-1\right)+\left(\dfrac{x-220}{19}-2\right)+\left(\dfrac{x-195}{21}-3\right)+\left(\dfrac{x-166}{23}-4\right)=0\)

=>x-258=0

=>x=258