\(\dfrac{x}{5}=\dfrac{2}{3}\)

\(\Leftrightarrow3x=10\)

\(\Leftrightarrow x=\dfrac{10}{3}\)

\(\left|3-x\right|\le2\)

\(\Leftrightarrow\left(3-x\right)^2\le4\)

\(\Leftrightarrow9-6x+x^2\le4\)

\(\Leftrightarrow x^2-6x+5\le0\)

\(\Leftrightarrow x^2-x-5x+5\le0\)

\(\Leftrightarrow x\left(x-1\right)-5\left(x-1\right)\le0\)

\(\Leftrightarrow\left(x-5\right)\left(x-1\right)\le0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-5\ge0\\x-1\le0\end{matrix}\right.\\\left\{{}\begin{matrix}x-5\le0\\x-1\ge0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\)\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge5\\x\le1\end{matrix}\right.\\\left\{{}\begin{matrix}x\le5\\x\ge1\end{matrix}\right.\end{matrix}\right.\)

Thấy TH2 thỏa mãn.

Vậy ...

\(B=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{98.99.100}\)

\(=1-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{98}-\dfrac{1}{99}-\dfrac{1}{100}=1-\dfrac{1}{100}=\dfrac{99}{100}\)

\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+2002\right)+2003=2003\)

\(\Leftrightarrow x+x+1+x+2+...+x+2002=0\)

\(\Leftrightarrow2003x+2005003=0\)

\(\Leftrightarrow2003x=-2005003\)

\(\Leftrightarrow x=-1001\)

2. 

a. 32

b. 81

c. 64

d. 625

3.

a. 5¹⁰

b. 3⁵

c. 5³

d. a³

e. a⁸

f. x¹²

g. 1

h. 9⁷

a. Có \(\widehat{D}=60^o\)

\(\Rightarrow\widehat{A}=180^o-60^o=120^o\) (2 góc trong cùng phía)

b. Có \(5\widehat{B}=4\widehat{C}\)

\(\Leftrightarrow\dfrac{\widehat{B}}{4}=\dfrac{\widehat{C}}{5}=\dfrac{\widehat{B}+\widehat{C}}{9}=\dfrac{180^o}{9}=20\)

\(\Leftrightarrow\left\{{}\begin{matrix}\widehat{B}=80^o\\\widehat{C}=100^o\end{matrix}\right.\)

Câu c là hỗn số nên không ngoặc 1 số còn phần phân số để ngoài đc đâu, toàn bộ hỗn số nằm trong ngoặc

\(a.0,6+-\dfrac{2}{3}=\dfrac{3}{5}-\dfrac{2}{3}=-\dfrac{1}{15}\)

\(b.\dfrac{1}{3}-\left(-0,4\right)=\dfrac{1}{3}+\dfrac{2}{5}=\dfrac{11}{5}\)

\(c.3,5.\left(-1\dfrac{2}{5}\right)=\dfrac{7}{2}.\left(-\dfrac{7}{5}\right)=-\dfrac{49}{10}\)

\(d.-\dfrac{5}{23}:\left(-2\right)=-\dfrac{5}{23}.\left(-\dfrac{1}{2}\right)=\dfrac{5}{46}\)

\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+20\right)=20\)

\(\Leftrightarrow x+x+1+x+2+...+x+20=20\)

\(\Leftrightarrow21x+210=20\)

\(\Leftrightarrow21x=-190\)

\(\Leftrightarrow x=-\dfrac{190}{21}\)