\(\left|x-\dfrac{1}{3}\right|+\dfrac{4}{5}=\left(-3,2\right)+\dfrac{2}{5}\)

\(\left|x-\dfrac{1}{3}\right|+\dfrac{4}{5}=-\dfrac{14}{5}\)

\(\left|x-\dfrac{1}{3}\right|=-\dfrac{14}{5}-\dfrac{4}{5}=-\dfrac{18}{5}\)

Vì \(\left|x-\dfrac{1}{3}\right|\ge0\) ∀x

⇒Phương trình vô nghiệm

|x-\(\dfrac{1}{3}\)|+\(\dfrac{4}{5}\)=|(\(\dfrac{-16}{5}\))+\(\dfrac{2}{5}\)|

⇒|x-\(\dfrac{1}{3}\)|+\(\dfrac{4}{5}\)=|\(\dfrac{-14}{5}\)|

⇒|x-\(\dfrac{1}{3}\)|+\(\dfrac{4}{5}\)=\(\dfrac{14}{5}\)

⇒|x-\(\dfrac{1}{3}\)|=\(\dfrac{14}{5}\)-\(\dfrac{4}{5}\)

⇒|x-\(\dfrac{1}{3}\)|=2

⇒x-\(\dfrac{1}{3}\)=2⇒x=\(\dfrac{7}{3}\)

hoặc

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

Vậy x=\(\dfrac{7}{3}\) hoặc x=\(\dfrac{-5}{3}\)

\(\dfrac{-5}{3}\)

=> |x-1/3| +4/5 = 0,7

=> |x-1/3|  = -3,8

mà |x-1/3|  \(\ge\)0

=> ko tồn tại x

mà[x-1/3] > 0 nha

\(|x-\frac{1}{3}|+\frac{4}{5}=|\left(-3,2\right)+\frac{2}{5}|\)

\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left|\frac{-16}{5}+\frac{2}{5}\right|\)

\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left|\frac{-14}{5}\right|\)

\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\frac{14}{5}\)

\(\Rightarrow\left|x-\frac{1}{3}\right|=\frac{14}{5}-\frac{4}{5}\)

\(\left|x-\frac{1}{3}\right|=\frac{10}{5}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\frac{1}{3}=\frac{-10}{5}\\x-\frac{1}{3}=\frac{10}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{-5}{3}\\x=\frac{7}{3}\end{matrix}\right.\)

Vậy: \(x\in\left\{\frac{-5}{3};\frac{7}{3}\right\}\)

Chúc bạn học tốt nhé !!!

∣ ∣ ∣ x − 1 3 ∣ ∣ ∣ + 4 5 = ∣ ∣ ∣ − 3.2 + 2 5 ∣ ∣ ∣ ⇒ ∣ ∣ ∣ x − 1 3 ∣ ∣ ∣ + 4 5 = ∣ ∣ ∣ − 28 5 ∣ ∣ ∣ ⇒ ∣ ∣ ∣ x − 1 3 ∣ ∣ ∣ + 4 5 = 28 5 ⇒ ∣ ∣ ∣ x − 1 3 ∣ ∣ ∣ = 28 5 − 4 5 = 24 5 ⇒ x − 1 3 = ( ± 24 5 ) ⇒ ⎡ ⎢ ⎢ ⎣ x − 1 3 = 24 5 x − 1 3 = − 24 5 ⇒ ⎡ ⎢ ⎢ ⎣ x = 24 5 + 1 3 x = − 24 5 + 1 3 ⇒ ⎡ ⎢ ⎢ ⎣ x = 77 15 x = − 67 15

\(\left|x-\dfrac{1}{3}\right|+\dfrac{4}{5}=\left|\left(-3,2\right)+\dfrac{2}{5}\right|\\ \Rightarrow\left|x-\dfrac{1}{3}\right|+\dfrac{4}{5}=\left|\dfrac{-14}{5}\right|\\ \Rightarrow\left|x-\dfrac{1}{3}\right|+\dfrac{4}{5}=\dfrac{14}{5}\\ \Rightarrow\left|x-\dfrac{1}{3}\right|=2\\ \Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=-2\\x-\dfrac{1}{3}=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-5}{3}\\x=\dfrac{7}{3}\end{matrix}\right.\)

Đổi 15 phút = 0,25 giờ

Quãng đường người đó đã đi được bằng xe máy là:

               40   \(\times\) 0,25 = 10 (km)

Quãng đường còn lại người đó đi bằng ô tô dài:

            145 - 10 = 135 (km)

Vận tốc của ô tô là:

              135 : 3 = 45 (km/h)

Đáp số: 45 km/h 

    3,2 \(\times\) 5 + 3,2 \(\times\) 4 + 0,2 \(\times\) 3,2 \(\times\) 5

= 3,2 \(\times\) ( 5 + 4 + 0,2 \(\times\) 5)

= 3,2 \(\times\) ( 9 + 1)

= \(3,2\) \(\times\) 10

= 32

\(3,2x-\left(\dfrac{4}{5}+\dfrac{2}{3}\right):3\dfrac{2}{3}=\dfrac{7}{20}\\ \Rightarrow\dfrac{16}{5}x-\dfrac{22}{15}:\dfrac{11}{3}=\dfrac{7}{20}\\ \Rightarrow\dfrac{16}{5}x-\dfrac{2}{5}=\dfrac{7}{20}\\ \Rightarrow\dfrac{16}{5}x=\dfrac{3}{4}\\ \Rightarrow x=\dfrac{15}{64}\)

\(\left(4\dfrac{1}{2}-2x\right).1\dfrac{4}{61}=6\dfrac{1}{2}\\ \Rightarrow\left(\dfrac{9}{2}-2x\right).\dfrac{65}{61}=\dfrac{13}{2}\\ \Rightarrow\dfrac{9}{2}-2x=\dfrac{61}{10}\\ \Rightarrow2x= -\dfrac{8}{5}\\ \Rightarrow x=-\dfrac{4}{5}\)