Ta có \(\dfrac{7-x}{13+y}=\dfrac{7}{13}\Rightarrow\dfrac{7-x}{7}=\dfrac{13+y}{13}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\dfrac{7-x}{7}=\dfrac{13+y}{13}=\dfrac{13+y-7+x}{13-7}=\dfrac{6+x+y}{6}=\dfrac{2022+6}{6}=338\)

\(\Rightarrow\left\{{}\begin{matrix}7-x=338\times7=2366\\13+y=338\times13=4394\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-2359\\y=4381\end{matrix}\right.\)

Ta có \(\dfrac{7-x}{13+y}=\dfrac{7}{13}\Rightarrow\dfrac{7-x}{7}=\dfrac{13+y}{13}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\dfrac{7-x}{7}=\dfrac{13+y}{13}=\dfrac{13+y-7+x}{13-7}=\dfrac{6+x+y}{6}=\dfrac{2022+6}{6}=338\)

\(\Rightarrow\left\{{}\begin{matrix}7-x=338\times7=2366\\13+y=338\times13=4394\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-2359\\y=4381\end{matrix}\right.\)

Tính đúng  y = 4 2 3

y = 4 2 3

13/15 - (13/21  + x) . 7/12 = 7/10

=> (13/21 + x). 7/12 = 13/15 - 7/10

=> (13/21 + x) . 7/12 = 1/6

=> 13/21 + x = 1/6 : 7/12

=> 13/21 + x = 2/7

=> x = 2/7 - 13/21

=> x = -1/3

\(a,\dfrac{2}{3}.x=\dfrac{2}{7}\\ x=\dfrac{2}{7}:\dfrac{2}{3}=\dfrac{3}{7}\\ ---\\ b,x.\dfrac{3}{5}=\dfrac{2}{5}\\ x=\dfrac{2}{5}:\dfrac{3}{5}=\dfrac{2}{3}\\ ---\\ c,x:\dfrac{8}{13}=\dfrac{13}{7}\\x=\dfrac{13}{7}.\dfrac{8}{13}=\dfrac{8}{7}\\ ----\\ d,\dfrac{3}{2}:x=\dfrac{7}{4}\\ x=\dfrac{3}{2}:\dfrac{7}{4}=\dfrac{3}{2}.\dfrac{4}{7}=\dfrac{6}{7}\)

\(|x-4|-13\)

\(\Leftrightarrow \left[\begin{array}{} x-4=13\\ x-4=-13 \end{array} \right.\)

\(\Leftrightarrow \left[\begin{array}{} x=13+4\\ x=(-13)+4 \end{array} \right.\)

\(\Leftrightarrow \left[\begin{array}{} x=17\\ x=-9 \end{array} \right.\)

 Vậy x ∈ {17;-9}

\(|x-4|-13=7\)

\(\Leftrightarrow |x-4|=7+13\)

\( \Leftrightarrow |x-4|=20\)

\(\Leftrightarrow \left[\begin{array}{} x-4=20\\ (x-4=-20 \end{array} \right.\)

\(\Leftrightarrow \left[\begin{array}{} x=20+4\\ x=(-20)+4 \end{array} \right.\)

\(\Leftrightarrow \left[\begin{array}{} x=24\\ x=-16 \end{array} \right.\)

Vậy x ∈{24;-16}

\(\left|\left|x-4\right|-13\right|=7\)

\(\Leftrightarrow\left[{}\begin{matrix}\left|x-4\right|-13=7\\\left|x-4\right|-13=-7\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left|x-4\right|=21\\\left|x-4\right|=6\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x-4=21\\x-4=-21\end{matrix}\right.\\\left[{}\begin{matrix}x-4=6\\x-4=-6\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=25\\x=-17\end{matrix}\right.\\\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.\end{matrix}\right.\)

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