`Answer:`

Bài 1:

a. \(-415.25-8=-10375-8=-10383\)

b. \(\left(-154\right).\left(-1625\right)=250250\)

c. \(-54.135=-7290\)

d. \(178:414=\frac{178}{414}=\frac{89}{207}\)

e. \(-209.513=-107217\)

f. \(-48:-245=\frac{48}{245}\)

Bài 2:

a. \(x+13=-73\Leftrightarrow x=-73-13\Leftrightarrow x=-86\)

b. \(x-113=-79\Leftrightarrow x=-79+113\Leftrightarrow x=34\)

c. \(2x+12=-53\Leftrightarrow2x=-53-12\Leftrightarrow2x=-65\Leftrightarrow x=-32,5\)

d. \(-59:x=169\Leftrightarrow x=-59:169\Leftrightarrow x=-\frac{59}{169}\)

Bài 3:

a. \(65+[3+\left(-15\right)]=65+3-15=\left(65-15\right)+3=53\)

b. \(\left(-57\right).211+\left(-57\right).911+157=\left(-57\right).\left(211+911\right)+157=-63954+157=-63797\)

c. \(819+421+25+1721+\left(-2719\right)=\left(819+1721\right)+\left(421-2719\right)+25=2540-2298+25=267\)

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

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}.x+\frac{1}{4}=0\\2.x-\frac{1}{3}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x=-\frac{1}{4}\\2x=\frac{1}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=\frac{1}{6}\end{cases}}\)

Vậy x = -1/2 hoặc x = 1/6

Mình nghĩ các bài trên là kiến thức đơn giản nên mình giải bài cuối nhé

\(A < \frac{1}{1.2}+ \frac{1}{2.3}+..+\frac{1}{9.10}\)

\(=\frac{1}{1}- \frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{9}-\frac{1}{10}=1-\frac{1}{10}=\frac{9}{10}\)

Mà \(\frac{9}{10}<1\)

\(=> A < \frac{9}{10} < 1\)

Tách ra đi bn

S=(131+132+...+140)+(141+...+150)+(151+...+160)

Mà (131+...+140)>140⋅10=14

Tương tự : (141+142+...+150)>15

(151+...+160)>16

S>14+15+16>35( x 1)

Mặt khác:(131+...+140)<131⋅10=13

⇒S<45⇒S<45( x 2)

*Bổ sung cái nãy:

Từ ( 1 ) và ( 2 ) => 3/5 < S < 4/5

\(\left(x-\dfrac{3}{5}\right)\left(25x^2-16\right)=0\Leftrightarrow x=\dfrac{3}{5};x=\dfrac{4}{5};x=-\dfrac{4}{5}\)

\(\left(x--\frac{3}{5}\right).\left(25.x^2-16\right)=0\)

\(\Leftrightarrow\left(x+\frac{3}{5}\right)\left(25.x^2-16\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{3}{5}=0\\25.x^2-16=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{5}\\x^2=\frac{16}{25}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{5}\\x=\frac{4}{5}\end{cases}}\)

Vậy x = -3/5 hoặc x = 4/5 

\(A = 3.(\frac{1}{3.5} + \frac{1}{5.7}+...+\frac{1}{99.101})\)

\(A = 3.(\frac{1}{3} - \frac{1}{5} + \frac{1}{5} - ....+\frac{1}{99} -\frac{1}{101})\)

\(A = 3.(\frac{1}{3} - \frac{1}{101})\)

\(A = 3.\frac{98}{303}\)

\(A=\frac{98}{101}\)

\(=> A<1\)