Lời giải:

$27^x+9^x=9^{25}$

$(3^3)^x+(3^2)^x=(3^2)^{25}$

$3^{3x}+3^{2x}=3^{50}$

$3^{3x+2x}=3^{50}$

$3^{5x}=3^{50}$

$\Rightarrow 5x=50$

$\Rightarrow x=10$

         C =   1 - 2 + 2² - 2³ + 2⁴ -...+ 2²⁰²²

       2C =       2 - 2² + 2³ - 2⁴ +...- 2²⁰²² + 2²⁰²³

2C + C = 2²⁰²³ + 1

      3C = 2²⁰²³ + 1

       C = \(\dfrac{2^{2023}+1}{3}\)

\(\dfrac{-13}{5}< \dfrac{7}{x}< \dfrac{-9}{4}\)

\(\Rightarrow\dfrac{-4}{9}< \dfrac{x}{7}< \dfrac{-5}{13}\)

\(\Rightarrow\dfrac{-4.7.13}{7.9.13}< \dfrac{9.13x}{7.9.13}< \dfrac{-5.7.9}{7.9.13}\)

\(\Rightarrow\dfrac{-364}{7.9.13}< \dfrac{117x}{7.9.13}< \dfrac{-315}{7.9.13}\)

\(\Rightarrow117x\in\left\{-363;-362;...;-314\right\}\)

\(\Rightarrow117x=-351\)

\(\Rightarrow x=-3\)

Vậy phân số đó là \(\dfrac{-7}{3}\)

tui học lớp 4 chứ có phải lớp 7 đâu.

\(M=2a-\dfrac{5b}{a}-3b\)

\(\dfrac{a}{b}=\dfrac{3}{5}\Rightarrow a=\dfrac{3}{5}b\) và \(\dfrac{b}{a}=\dfrac{5}{3}\)

\(\Rightarrow M=2.\dfrac{3}{5}b-5.\dfrac{5}{3}-3b\)

\(\Rightarrow M=\dfrac{6}{5}b-3b-\dfrac{25}{3}\)

\(\Rightarrow M=\left(\dfrac{6}{5}-3\right)b-\dfrac{25}{3}\)

\(\Rightarrow M=\dfrac{-9}{5}b-\dfrac{25}{3}\)

`@` `\text {Ans}`

`\downarrow`

\(\dfrac{253}{-254}=\dfrac{-253}{254}\)

\(-\dfrac{1234}{1232}=\dfrac{-617}{616}\)

Ta có: \(\dfrac{617}{616}>1\) ; \(\dfrac{253}{254}< 1\)

`=>`\(\dfrac{617}{616}>\dfrac{253}{254}\)

`=>`\(\dfrac{-617}{616}< \dfrac{-253}{254}\)

Vậy, \(\dfrac{253}{-254}>\dfrac{-1234}{1232}\).

\(MSC=254.1232\)

\(\dfrac{253}{-254}=\dfrac{-253}{254}=\dfrac{-253.1232}{254.1232}=\dfrac{\text{-311696}}{254.1232}\)

\(\dfrac{-1234}{1232}=\dfrac{-1234.254}{254.1232}=\dfrac{\text{-313436}}{254.1232}\)

mà \(\dfrac{\text{-313436}}{254.1232}< \dfrac{\text{-311696}}{254.1232}\)

\(\Rightarrow\dfrac{-1234}{1232}< \dfrac{253}{-254}\)

\(\)

cần gấp!!!

lâu thế!!

`@` `\text {Ans}`

`\downarrow`

\(\dfrac{1}{3}\div x=-\dfrac{5}{7}-\left(-\dfrac{2}{3}\right)\)

`=>`\(\dfrac{1}{3}\div x=-\dfrac{5}{7}+\dfrac{2}{3}\)

`=>`\(\dfrac{1}{3}\div x=-\dfrac{1}{21}\)

`=>`\(x=\dfrac{1}{3}\div\left(-\dfrac{1}{21}\right)\)

`=> x = -7`

Vậy `x = -7.`

1/3:x=-5/7- -2/3
1/3:x=-1/21
      x=1/3: (-1/21)
      x=-7

,làm ơn giúp mik với ah

\(\left(1+\dfrac{2}{3}\right).\left(1+\dfrac{2}{4}\right).\left(1+\dfrac{2}{5}\right)....\left(1+\dfrac{2}{2020}\right).\left(1+\dfrac{2}{2021}\right)\)

= \(\dfrac{5}{3}.\dfrac{6}{4}.\dfrac{7}{5}.\dfrac{8}{6}.\dfrac{9}{7}....\dfrac{2022}{2020}.\dfrac{2023}{2021}\)

= \(\dfrac{1}{3}.\dfrac{1}{4}.2022.2023\)

= \(\dfrac{337.2023}{2}\)

= \(\dfrac{\text{681751}}{2}\)

`@` `\text {Ans}`

`\downarrow`

\(\dfrac{7}{4}x+\dfrac{2}{3}=\dfrac{5}{6}\)

`\Rightarrow`\(\dfrac{7}{4}x=\dfrac{5}{6}-\dfrac{2}{3}\)

`\Rightarrow`\(\dfrac{7}{4}x=\dfrac{1}{6}\)

`\Rightarrow`\(x=\dfrac{1}{6}\div\dfrac{7}{4}\)

`\Rightarrow` `x=2/21`

Vậy, `x = 2/21.`

\(\dfrac{7}{4}.x+\dfrac{2}{3}=\dfrac{5}{6}\)

⇒\(\dfrac{7}{4}.x=\dfrac{5}{6}-\dfrac{2}{3}=\dfrac{1}{6}\)

⇒\(x=\dfrac{1}{6}:\dfrac{7}{4}=\dfrac{1}{6}.\dfrac{4}{7}=\dfrac{2}{21}\)

`@` `\text {Ans}`

`\downarrow`

\(\left(\dfrac{17}{5}+\dfrac{3}{4}\right)\cdot\left(-\dfrac{1}{2}-\dfrac{4}{3}\right)\)

`=`\(\dfrac{83}{20}\cdot\left(-\dfrac{11}{6}\right)=-\dfrac{913}{120}\)

  (\(\dfrac{17}{5}\) + \(\dfrac{3}{4}\)).(-\(\dfrac{1}{2}\) - \(\dfrac{4}{3}\))

=( \(\dfrac{68}{20}\) + \(\dfrac{15}{20}\)).(- \(\dfrac{3}{6}\) - \(\dfrac{8}{6}\))

= \(\dfrac{83}{20}\).(\(-\dfrac{11}{6}\))

= - \(\dfrac{913}{120}\)