9. Has the work been done by him?

10. The boxes were opened and cigarettes were taken out by us

11. She was given a new one

12. He is proved wrong

13. We were promised higher wages

14. This is the third time we have been written to about this by them

15. We were asked to be there at 8 o'clock

16. She is being shown how to do it

c. \(\left|\dfrac{8}{4}-\left|x-\dfrac{1}{4}\right|\right|-\dfrac{1}{2}=\dfrac{3}{4}\)

\(\Rightarrow\left[{}\begin{matrix}\left|\dfrac{8}{4}-x+\dfrac{1}{4}\right|-\dfrac{1}{2}=\dfrac{3}{4}\\\left|\dfrac{8}{4}+x-\dfrac{1}{4}\right|-\dfrac{1}{2}=\dfrac{3}{4}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left|\dfrac{9}{4}-x\right|-\dfrac{1}{2}=\dfrac{3}{4}\\\left|\dfrac{7}{4}+x\right|-\dfrac{1}{2}=\dfrac{3}{4}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}\dfrac{9}{4}-x-\dfrac{1}{2}=\dfrac{3}{4}\\x=\dfrac{9}{4}-\dfrac{1}{2}=\dfrac{3}{4}\end{matrix}\right.\\\left[{}\begin{matrix}\dfrac{7}{4}+x-\dfrac{1}{2}=\dfrac{3}{4}\\-\dfrac{7}{4}-x-\dfrac{1}{2}=\dfrac{3}{4}\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=1\\x=\dfrac{7}{2}\end{matrix}\right.\\\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=-3\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{7}{2}\\x=-3\end{matrix}\right.\) 

Ở nơi x=9/4-1/2 là x-9/4-1/2 nha

a. -1,5 + 2x = 2,5

<=> 2x = 2,5 + 1,5

<=> 2x = 4

<=> x = 2

b. \(\dfrac{3}{2}\left(x+5\right)-\dfrac{1}{2}=\dfrac{4}{3}\)

<=> \(\dfrac{3}{2}x+\dfrac{15}{2}-\dfrac{1}{2}=\dfrac{4}{3}\)

<=> \(\dfrac{9x}{6}+\dfrac{45}{6}-\dfrac{3}{6}=\dfrac{8}{6}\)

<=> 9x + 45 - 3 = 8

<=> 9x = 8 + 3 - 45

<=> 9x = -34

<=> x = \(\dfrac{-34}{9}\)

Đặt \(A=1^3+2^3+3^3+...+99^3+100^3\)

\(\Rightarrow A=\left(1-1\right).1.\left(1+1\right)+1+\left(2-1\right).2.\left(2+1\right)+2+...+\left(99-1\right).99.\left(99+1\right)+99+\left(100-1\right).100.\left(100+1\right)+100\)

\(\Rightarrow A=1+2+1.2.3+3+2.3.4+...+100+99.100.101\)

\(\Rightarrow A=\left(1+2+3+...+100\right)+\left(1.2.3+2.3.4+...+99.100.101\right)\)

\(\Rightarrow A=5050+101989800\)

\(\Rightarrow A=101994850.\)

Vậy \(A=101994850.\)

Chúc bạn học tốt!

a, \(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{x\cdot\left(x+1\right)\cdot\left(x+2\right)}=\frac{2018}{2019}\)

\(=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot3}+...+\frac{1}{x\cdot\left(x+1\right)}-\frac{1}{\left(x+1\right)\cdot\left(x+2\right)}=\frac{2018}{2019}\)

\(=1-\frac{1}{\left(x+1\right)\cdot\left(x+2\right)}=\frac{2018}{2019}\)

\(\Rightarrow\frac{1}{\left(x+1\right)\cdot\left(x+2\right)}=1-\frac{2018}{2019}\)

\(\Rightarrow\frac{1}{\left(x+1\right)\cdot\left(x+2\right)}=\frac{2019}{2019}-\frac{2018}{2019}=\frac{1}{2019}\)

Đến đây bn tự tính nhé !!

Nhưng \(\frac{1}{1.2.3}\)ko bằng \(\frac{1}{1.2}-\frac{1}{2.3}\)ạ

Bn có thể suy nghĩ lại giúp mik đc ko????

- Ấy chết mk quên, bn đưa \(\frac{1}{2}\cdot\left(...\right)\)

Vào nữa nhé. Mk thử lại nek:

\(\frac{1}{1\cdot2\cdot3}=\frac{1}{6}\)và \(\frac{1}{2}\cdot\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}\right)=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{6}\right)\)

\(=\frac{1}{2}\cdot\left(\frac{3}{6}-\frac{1}{6}\right)=\frac{1}{2}\cdot\frac{2}{6}=\frac{2}{12}=\frac{1}{6}\)nhé bn !!

b)

Phân số là số nguyên <=> \(-3⋮2n-1\)

<=> \(2n-1\inƯ\left(-3\right)\)

Ta có bảng:

KL: \(n\in\left\{1;0;2;-1\right\}\)

c) \(\frac{n+4}{n+1}=\frac{\left(n+1\right)+3}{n+1}\) = \(1+\frac{3}{n+1}\)

Để phân số là số nguyên <=> \(1+\frac{3}{n+1}\) là số nguyên

<=> \(\frac{3}{n+1}\) là số nguyên

Rồi bạn lm tương tự như ở câu b)

a: =>12x+5(x-1)=100-10(3x-1)

=>12x+5x-5=100-30x+30

=>17x-5=-30x+130

=>47x=135

=>x=135/47

b: \(\Leftrightarrow6\left(2x-1\right)+2\left(5-x\right)=24-9\left(x+1\right)\)

=>12x-6+10-2x=24-9x-9

=>10x+4=-9x+15

=>19x=11

=>x=11/19