\(1\dfrac{2}{3}-\left(3\dfrac{1}{2}-x\right)=\dfrac{5}{9}\)

\(\dfrac{7}{2}-x=\dfrac{5}{3}-\dfrac{5}{9}\)

\(\dfrac{7}{2}-x=\dfrac{10}{9}\)

\(x=\dfrac{7}{2}-\dfrac{10}{9}\)

\(x=\dfrac{43}{18}\)

\(\dfrac{-3}{4}\times23\dfrac{11}{23}-\dfrac{3}{4}\times8\dfrac{12}{23}\\ =\dfrac{-3}{4}\times\left(23\dfrac{11}{23}+8\dfrac{12}{23}\right)\\ =\dfrac{-3}{4}\times32\\ =\dfrac{-96}{4}\\ =-24\)

\(\dfrac{-3}{4}\times23\dfrac{11}{23}-\dfrac{3}{4}\times8\dfrac{12}{23}\\ =\dfrac{-3}{4}\times\left(23\dfrac{11}{23}+8\dfrac{12}{23}\right)\\ =\dfrac{-3}{4}\times32\\ =\dfrac{-96}{4}\\ =-18\)

\(\dfrac{2}{3}:\left(x-\dfrac{5}{2}\right)=\dfrac{8}{9}\)

\(\Rightarrow x-\dfrac{5}{2}=\dfrac{2}{3}:\dfrac{8}{9}\\ \Rightarrow x-\dfrac{5}{2}=\dfrac{3}{4}\\ \Rightarrow x=\dfrac{3}{4}+\dfrac{5}{2}\\ \Rightarrow x=\dfrac{3}{4}+\dfrac{10}{4}\\ \Rightarrow x=\dfrac{13}{4}\)

Bài 3

\(M=\dfrac{100^{100}+1}{100^{99}+1}=\dfrac{100^{100}+100-9}{100^{99}+1}=100-\dfrac{99}{100^{99}+1}\)

\(N=\dfrac{100^{101}+1}{100^{100}+1}=\dfrac{100^{101}+100-99}{100^{100}+1}=100-\dfrac{99}{100^{100}+1}\)

\(\rightarrow M< N\)

Bài 2

\(a,x+\dfrac{1}{3}=-\dfrac{5}{6}\\ \Rightarrow x=-\dfrac{5}{6}-\dfrac{1}{3}\\ \Rightarrow x=-\dfrac{5}{6}-\dfrac{2}{6}\\ \Rightarrow x=-\dfrac{7}{6}\)

\(b,\left(x-\dfrac{3}{5}\right):\dfrac{-1}{3}=0,4\\ \Rightarrow x-\dfrac{3}{5}=\dfrac{2}{5}\cdot\dfrac{-1}{3}\\ \Rightarrow x-\dfrac{3}{5}=-\dfrac{2}{15}\\ \Rightarrow x=-\dfrac{2}{15}+\dfrac{3}{5}\\ \Rightarrow x=\dfrac{7}{15}\)

\(c,\left(-\dfrac{3}{5}\right)^7:x=\left(-0,6\right)^3\cdot0,36\\ \left(-\dfrac{3}{5}\right)^7:x=\left(-\dfrac{3}{5}\right)^3.\left(-\dfrac{3}{5}\right)^2\\ \left(-\dfrac{3}{5}\right)^7:x=\left(-\dfrac{3}{5}\right)^5\\ x=\left(-\dfrac{3}{5}\right)^2\\ x=\dfrac{9}{25}\)

\(\dfrac{1}{2}x-x+20\%x=2\dfrac{1}{4}\)

\(\Rightarrow\left(\dfrac{1}{2}-1+\dfrac{1}{5}\right)x=\dfrac{9}{4}\)

\(\Rightarrow-\dfrac{3}{10}x=\dfrac{9}{4}\)

\(\Rightarrow x=\dfrac{9}{4}:\dfrac{-3}{10}\)

\(\Rightarrow x=\dfrac{-15}{2}\)

\(\rightarrow\) Có

\(+\) Phân số viết dưới dạng  \(\dfrac{a}{b}\) (biết \(b\ne0\))

Nửa chu vi mảnh vườn hình chữ nhật là:

\(104:2=52\left(m\right)\)

Chiều dài mảnh vườn hình chữ nhật là:

\(\left(52+14\right):2=33\left(m\right)\)

Chiều rộng mảnh vườn hình chữ nhật là:

\(33-14=19\left(m\right)\)

a, Diện tích mảnh vườn hình chữ nhật là:

\(33\times19=627\left(m^2\right)\)

b,Số kg rau thu hoạch được trên mảnh vườn là:

\(627:1\times5=3135\left(kg\right)\)

Đáp số:  \(a,627m^2;b,3135kg\) rau

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

\(\Rightarrow\left(\dfrac{2}{3}-\dfrac{1}{6}\right)x=\dfrac{5}{4}\)

\(\Rightarrow\left(\dfrac{4}{6}-\dfrac{1}{6}\right)x=\dfrac{5}{4}\)

\(\Rightarrow\dfrac{1}{2}x=\dfrac{5}{4}\)

\(\Rightarrow x=\dfrac{5}{4}:\dfrac{1}{2}\)

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

Vậy: \(x=\dfrac{5}{2}\)