\(\dfrac{11}{3}-\dfrac{3}{11}=\dfrac{121}{33}-\dfrac{99}{33}=\dfrac{121-99}{33}=\dfrac{22}{33}\)

\(a\)\(.\)\(7^2.5-\left(2x+1\right)=630:9\)

\(49.5-\left(2x+1\right)=70\)

\(245-\left(2x+1\right)=70\)

                 \(2x+1=245-70\)

                  \(2x+1=175\)

                   \(2x=175-1\)

                   \(2x=174\)

                   \(x=174:2\)

                   \(x=87\)

Vậy \(x=87\)

\(b.\)\(\left(10-4x\right)+120:2^3=17\)

        \(\left(10-4x\right)+120:8=17\)

         \(\left(10-4x\right)+15=17\)

          \(10-4x=17-15\)

           \(10-4x=2\)

           \(4x=10-2\)

            \(4x=8\)

            \(x=8:4\)

            \(x=2\)

Vậy \(x=2\)

\(c.\)\(\left[124-\left(20-4x\right)\right]:30+7=11\)

\(\left[124-\left(20-4x\right)\right]:30=11-7\)

\(\left[124-\left(20-4x\right)\right]:30=4\)

\(\left[124-\left(20-4x\right)\right]=4.30\)

\(\left[124-\left(20-4x\right)\right]=120\)

\(124-20+4x=120\)

\(104+4x=120\)

\(4x=120-104\)

\(4x=16\)

\(x=16:4\)

\(x=4\)

Vậy \(x=4\)

\(d.\)\(\left|2x+5\right|=1\)

\(\Rightarrow2x+5\in\left\{-1;1\right\}\)

\(\Rightarrow2x\in\left\{-6;-4\right\}\)

\(\Rightarrow x\in\left\{-3;-2\right\}\)

Vậy \(x\in\left\{-3;-2\right\}\)

học tốt

a) \(7^2\cdot5-\left(2x+1\right)=630:9\)

\(\Leftrightarrow49\cdot5-2x-1=70\)

\(\Leftrightarrow244-2x=70\)

\(\Leftrightarrow2x=244-70\)

\(\Leftrightarrow2x=174\)

\(\Leftrightarrow x=87\)

Vậy x=87.

b) \(\left(10-4x\right)+120:2^3=17\)

\(\Leftrightarrow10-4x+120:8=17\)

\(\Leftrightarrow10-4x+15=17\)

\(\Leftrightarrow25-4x=17\)

\(\Leftrightarrow4x=25-17=8\)

\(\Leftrightarrow x=2\)

Vậy x=2

c)\([124-\left(20-4x\right)]:30+7=11\)

\(\Leftrightarrow\left(124-20+4x\right):30=4\)

\(\Leftrightarrow104+4x=120\)

\(\Leftrightarrow4x=120-104=16\)

\(\Leftrightarrow x=4\)

Vậy x=4

d) \(|2x-5|=1\)

\(\Leftrightarrow\orbr{\begin{cases}2x-5=1\\2x-5=-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x=6\\2x=4\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=3\\x=2\end{cases}}\)

Vậy \(x\in\text{ }\left\{3;2\right\}\)

Sorry mình ghi nhầm đề bài phần d

Bổ sung đề bài : Tính

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=1-\frac{1}{7}=\frac{6}{7}\)

..................

\(501^2=501\times501=251001\)

501 ² = 251001

=251001

\(\sqrt{4x^2-4x+9}=3\\ \Rightarrow4x^2-4x+9=9\\ \Rightarrow4x\left(x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}4x=0\\x-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

Ta có: \(\sqrt{4x^2-4x+9}=3\)

\(\Leftrightarrow4x^2-4x=0\)

\(\Leftrightarrow4x\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

2³⁰ = (2³)¹⁰ = 8¹⁰

3²⁰ = (3²)¹⁰ = 9¹⁰

Vì 8¹⁰ < 9¹⁰ nên 2³⁰ < 3²⁰

Ta có: 2^30= 2^3.10= (2^3)^10= 8^10

3^20= 3^2.10= (3^2)^10= 9^10

Vì 8<9 nên 8^10<9^10

=> 2^30<3^20

2³⁰ = (2³)¹⁰ = 8¹⁰

3²⁰ = (3²⁾¹⁰  = 9¹⁰

Vì 8¹⁰ < 9¹⁰ nên 2³⁰ < 3²⁰

\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=1-\frac{1}{7}\)

\(=\frac{6}{7}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{42}\)

=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{6.7}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.........+\frac{1}{6}-\frac{1}{7}\)

=\(1-\frac{1}{7}\)

=\(\frac{6}{7}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}=1-\frac{1}{7}=\frac{6}{7}\)

Lời giải:
$1+2+3+....+25$

$=(1+25)+(2+24)+(3+23)+(4+22)+(5+21)+(6+20)+(7+19)+(8+18)+(9+17)+(10+16)+(11+15)+(12+14)+13$

$=\underbrace{26+26+26+...+26}_{12}+13$

$=26\times 12+13=325$

1/48+2/48+3/48+...7/48+8/48+9/48 >>1+2+3+4+5+6+7+8+9/48 = Đáp số

1+2+3+4+5+6+7+8+9=(1+9)+(2+8)+(3+7)+(4+6)+5

                               =10x4+5

                               =45

Suy ra bằng :45/48=15/16

=45 nha